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NCERT Solutions for Class 8 Mathematics Chapter 11 Mensuration

NCERT Solution For Class 8 Mathematics

Mensuration Here is the CBSE Mathematics Chapter 11 for Class 8 students. Summary and detailed explanation of the lesson, including the definitions of difficult words. All of the exercises and questions and answers from the lesson's back end have been completed. NCERT Solutions for Class 8 Mathematics Mensuration Chapter 11 NCERT Solutions for Class 8 Mathematics Mensuration Chapter 11 The following is a summary in Hindi and English for the academic year 2023-24. You can save these solutions to your computer or use the Class 8 Mathematics.

Question 1

NCERT Solutions for Class 8 Mathematics Chapter 11 Mensuration

NCERT Solution For Class 8 Mathematics

(a) Match the following figures with their respective areas in the box.(b) Write the perimeter of each shape.

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

Mrs. Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of Rs 55 per m2.

The shape of a garden is rectangular in the middle and semi-circular at the ends as shown in the diagram. Find the area and the perimeter of this garden. [Length of rectangle is 20 - (3.5 + 3.5) meters.]

A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles area required to cover a floor of area 1080 m2?(If required you can split the tiles in whatever way want to fill up the corners.)

An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression where r is the radius of the circle.

Nazma’s sister also has a trapezium shaped plot. Divide it into three parts as shown. Show that the area of trapezium WXYZ =

If h = 10 cm, c = 6 cm, b = 12 cm, d = 4 cm, find the values of each of its parts separately and add to find the area WXYZ. Verify it by putting the values of h, a and b in the expression

Find the area of the following trapezium:

Find the area of the following trapezium:

We know that parallelogram is also a quadrilateral. Let us also split such a quadrilateral into two triangles, find their areas and hence that of the parllelogram. Does this agree with the formula that you know already?

Find the area the quadrilateral LMNOP (as shown in the figure).

A parallelogram is divided into two congruent triangles by drawing a diagonal across it. Can we divide a trapezium into two congruent triangles?

Find the area of a rhombus whose diagonals are 12 cm and 9.2 cm.

Find the area of these quadrilaterals:

Divide the following polygons into parts (triangles and trapezium) to find out its area.

Find the area of polygon MNOPQR if MP = 9 cm, MD = 7 cm, MC = 6 cm, MB = 4 cm, MA = 2cm. NA, QC, QD and RB are perpendiculars to diagonal MP.

The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1 m and 1.2 m and perpendicular distance between them is 0.8 m.

The area of a trapezium is 34 cm2 and the length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the other parallel side.

Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 cm, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.

The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.

The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.

Find the area of a rhombus whose side is 5 cm and whose altitude is 4.8 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.

The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per m2 is Rs 4.

Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along road. If the area of his field is 10500 m2 and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

Top surface of a raised platform is in the shape of regular octagon as shown in the figure. Find the area of the octagonal surface.

There is a pentagonal shaped park as shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways.Find the area of this park using both ways. Can you suggest some other way of finding its area?

Fill in the blanks:

Find the area of the following figures.

Find the area of quadrilateral PQRS shown in the figure:

Find the area of a rhombus whose diagonals are of lengths 10 cm and 8.2 cm.

Find the area of the polygon ABCDE as shown in the figure.

The area of a trapezium shaped field is 480 m2, the distance between two parallel sides is 15 m and one of the parallel side is 20 m. Find the other parallel side.

The area of the rhombus is 240 cm2 and one of the diagonals is 16 cm. Find the other diagonal.

Find the area of the regular hexagon MNOPQR of side 5 cm.

Why is it incorrect to call the solid shown here a cylinder?

Find the total surface area of the following cuboids:

Can we say that the total surface area of cuboid = lateral surface area + 2 × area of base?

Find the surface area of cube A and lateral surface area of cube B.

Two cubes each with side b are joined to form a cuboid figure. What is the surface area of this cuboid? Is it 12b2? Is the surface area of cuboid formed by joining three such cubes, 18b2? why?

How will you arrange 12 cubes of equal length to form a cuboid of smallest surface area?

After the surface area of a cube is painted the cube is cut into 64 smaller cubes of same dimensions. How many have no face painted? 1 face painted? 2 faces painted? 3 faces painted?

Find total surface area of the following cylinders.

Note that lateral surface area of a cylinder is the circumference of base x height of cylinder. Can we write lateral surface area of a cuboid as perimeter of base x height of cuboid?

There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?

A suitcase with measures 80 cm × 48 cm × 24 cm is to be covered with a tarpaulin cloth. How many metres of tarpaulin of width 96 cm is required to cover 100 such suitcases?

Find the side of a cube whose surface area is 600 cm2.

Rukhsar painted the outside of the cabinet of measure 1 m × 2 m × 1.5 m. How much surface area did she cover if she painted all except bottom of the cabinet.

Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint 100 m2 of area is painted. How many cans of paint will she need to paint the room ?

Describe how the two figures at the right are alike and how they are different. Which box has larger surface area?

A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How much sheet of metal is required?

The lateral surface area of a hollow cylinder is 4224 cm2. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?

A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.

A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container as shown in the figure. If the label is placed 2 cm from top and bottom, what is the area of the label?

The length, breadth and height of a cuboid are 20 cm, 15 cm and 10 cm respectively. Find its total surface area.

An aquarium is in the form of a cuboid whose external measures are 80 cm x 30 cm x 40 cm. The base, side faces and back faces are to be covered with a coloured paper. Find the area of the paper needed.

The internal measures of a room are 12 m x 8 m x 4 m. Find the total cost of white washing all four walls of a room if the cost of white washing is Rs 5 per m2. What will be the cost of white washing if the ceiling is also white washed?

In a building there are 24 cylindrical pillars. The radius of each pillar is 28 cm and height is 4 m. Find the total cost of painting the curved surface area of all pillars at the rate of Rs 8 per m2.

Find the height of a cylinder whose radius is 7 cm and the total surface area is 968 cm2.

Find the volume of the following cuboids.

Find the volume of the following cubes. (a) with a side 4 cm (b) with a side 1.5 m.

A company sells biscuits. For packing purpose they are using cuboidal boxes: box A 3 cm x 8 cm x 20 cm, box B 4 cm x 12 cm x 10 cm. What size of the box will be economical for the company? why? Can you suggest any other size (dimensions) which has the same volume but is more economical than these?

Find the volume of the following cylinders.

Given a cylindrical tank, in which situation will you find surface area and in which situation volume.(a) To find how much it can hold.(b) Number of cement bags required to plaster it.(c) To find the number of smaller tanks that can be filled with water from it.

Find the height of a cuboid whose base area is 180 cm2 and volume is 900 cm3.

A cuboid is of dimensions 60 cm X 54 cm x 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?

Find the height of the cylinder whose volume is 1.54 m3 and diameter of the base is 140 cm?

A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank?

If each of a cube is doubled,(i) How many times will its surface area increase?(ii) How many times will its volume increase?

Water is pouring into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m3, find the number of hours it will take to fill the reservoir.

Fill in the blanks.(i) 1 cm3 = 1 cm x 1 cm x 1 cm = ....mm3(ii) 1 m3 = 1 m x 1 m x 1 m = ......cm3

Fill in the blanks.

Find the height of a cuboid whose volume is 275 cm3 and base area is 25 cm2.

A godown is in the form of a cuboid of measures 60 m × 40 m × 30 m. How many cuboidal boxes can be stored in it if the volume of one box is 0.8 m3?

A rectangular paper of width 14 cm is rolled along its width and a cylinder of radius 20 cm is formed. Find the volume of the cylinder. (Take )

A rectangular piece of paper is having measures 11 cm × 4 cm. It is folded without overlapping to make a cylinder of height 4 cm. Find the volume of the cylinder.

A rectangle and a square have equal perimeter. If the breadth of the rectangle is 10 cm and the side the square is 15 cm, then find the difference between their areas.

Find the area of the following trapezium.

(a) Match the following figures with their respective areas in the box.

(b) Write the perimeter of each shape.

Mrs. Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of Rs 55 per m².

A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles area required to cover a floor of area 1080 m²?
(If required you can split the tiles in whatever way want to fill up the corners.)

An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression $straight c equals 2 πr comma$ where r is the radius of the circle.

Nazma’s sister also has a trapezium shaped plot. Divide it into three parts as shown. Show that the area of trapezium WXYZ = $straight h fraction numerator left parenthesis straight a plus straight b right parenthesis over denominator 2 end fraction.$

The area of a trapezium is 34 cm² and the length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the other parallel side.

The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per m² is Rs 4.

Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along road. If the area of his field is 10500 m² and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

There is a pentagonal shaped park as shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways.

Find the area of this park using both ways. Can you suggest some other way of finding its area?

The area of a trapezium shaped field is 480 m², the distance between two parallel sides is 15 m and one of the parallel side is 20 m. Find the other parallel side.

The area of the rhombus is 240 cm² and one of the diagonals is 16 cm. Find the other diagonal.

Two cubes each with side b are joined to form a cuboid figure. What is the surface area of this cuboid? Is it 12b²? Is the surface area of cuboid formed by joining three such cubes, 18b²? why?

Find the side of a cube whose surface area is 600 cm².

Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint 100 m² of area is painted. How many cans of paint will she need to paint the room ?

The lateral surface area of a hollow cylinder is 4224 cm². It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?

The internal measures of a room are 12 m x 8 m x 4 m. Find the total cost of white washing all four walls of a room if the cost of white washing is Rs 5 per m². What will be the cost of white washing if the ceiling is also white washed?

In a building there are 24 cylindrical pillars. The radius of each pillar is 28 cm and height is 4 m. Find the total cost of painting the curved surface area of all pillars at the rate of Rs 8 per m².

Find the height of a cylinder whose radius is 7 cm and the total surface area is 968 cm².

Find the volume of the following cubes.
(a) with a side 4 cm (b) with a side 1.5 m.

Given a cylindrical tank, in which situation will you find surface area and in which situation volume.
(a) To find how much it can hold.
(b) Number of cement bags required to plaster it.
(c) To find the number of smaller tanks that can be filled with water from it.

Find the height of a cuboid whose base area is 180 cm² and volume is 900 cm³.

Find the height of the cylinder whose volume is 1.54 m³ and diameter of the base is 140 cm?

If each of a cube is doubled,
(i) How many times will its surface area increase?
(ii) How many times will its volume increase?

Water is pouring into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m³, find the number of hours it will take to fill the reservoir.

Fill in the blanks.
(i) 1 cm³ = 1 cm x 1 cm x 1 cm = ....mm³
(ii) 1 m³ = 1 m x 1 m x 1 m = ......cm³

Find the height of a cuboid whose volume is 275 cm³ and base area is 25 cm².

A godown is in the form of a cuboid of measures 60 m × 40 m × 30 m. How many cuboidal boxes can be stored in it if the volume of one box is 0.8 m³?

A rectangular paper of width 14 cm is rolled along its width and a cylinder of radius 20 cm is formed. Find the volume of the cylinder. (Take $straight pi equals 22 over 7$ )

Find the length of the diagonal BD when, the area of the quadrilateral is 32 cm².

A company is selling its suitcases according to their surface areas. A suitcase can be bought at the rate of Rs 0.05 per cm². If the size of the suitcase purchased by Ramita is 80 cm × 48 cm × 24 cm, find the cost paid by Ramita for such 100 suitcases.

The area of a trapezium is 0.88 m². If its parallel sides are 1.2 m and 1 m. then find its height.

The area of a quadrilateral shaped field is 252 m². The perpendiculars drawn on it from the opposite corners on a diagonal are 8 m and 13 m. Find the length of the diagonal.

Find the radius of the base of a cylinder whose volume and height are 1.54 cm² and 1 m respectively.

Find the base area of a cuboid whose volume and height are 900 cm³ and 5 cm respectively.

The area of a parallelogram is given by:

Base x Height

$1 half cross times Base space straight x space Height$

2 x Base x Height

Area of a trapezium is given by:

2 x Height x (Sum of the parallel sides)

Height x (Sum of the parallel sides)

$1 half cross times Height cross times left parenthesis Sum space of space the space parallel space sides right parenthesis$

The surface area of a right circular cylinder is given by:
$πr squared straight h$
$2 πr left parenthesis straight r plus straight h right parenthesis$
$space space space space space space 1 half πr left parenthesis straight r plus straight h right parenthesis$

The edge of a cube is 1 m. Its surface area is given by:
1 m²
6 m²
6 m³

The edge of a cube is 1 m. Its Its volume is given by:
1 m³
6 m³
3 m³

The perimeter of a square is 4 m. Its area is given by:
4 m²
2 m²
1 m²

The sum of the parallel sides of a trapezium is 8 cm. If its height is 2 cm. then its area is given by:
8 cm²
16 cm²
32 cm²

In a parallelogram, base = height = 1 cm. What its area?
1 cm²
2 cm²
3 cm²

What is the surface area of a cylinder whose radius = $space 7 over 2 space cm space$ and height = 7 cm?

154 cm²

308 cm²

77 cm²