The difference between outside and inside surface of a cylindrical metallic pipe 14 cm long is 44 cm 2 . If the pipe is made of 99 cm 3 of metal, find the outer and inner radii of the pipe. - Wired Faculty

Probability

Question

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The difference between outside and inside surface of a cylindrical metallic pipe 14 cm long is 44 cm². If the pipe is made of 99 cm³ of metal, find the outer and inner radii of the pipe.

Solution

Let the outer and inner radii of the pipe be R cm and r cm respectively. Then,

2 πR left parenthesis 14 right parenthesis minus 2 πr left parenthesis 14 right parenthesis equals 44

rightwards double arrow space space space space space space 28 straight pi space left parenthesis straight R minus straight r right parenthesis equals 44

rightwards double arrow space space space space space space 28 cross times 22 over 7 left parenthesis straight R minus straight r right parenthesis equals 44

rightwards double arrow

straight R minus straight r equals 1 half space space space space space space space space space space... left parenthesis 1 right parenthesis

and,

πR squared left parenthesis 14 right parenthesis minus πr squared left parenthesis 14 right parenthesis equals 99

rightwards double arrow space space space space space space 14 straight pi space left parenthesis straight R squared minus straight r squared right parenthesis equals 99

rightwards double arrow space space space space space space space space space 14 cross times 22 over 7 left parenthesis straight R squared minus straight r squared right parenthesis space equals space 99 rightwards double arrow space space space space space space space space space left parenthesis straight R plus straight r right parenthesis left parenthesis straight R minus straight r right parenthesis equals 9 over 4 rightwards double arrow space space space space space space space space space space left parenthesis straight R plus straight r right parenthesis 1 half equals 9 over 4 space space space space space space vertical line space From space left parenthesis straight i right parenthesis rightwards double arrow space space space space space space space space space space straight R plus straight r equals 9 over 2 space space space space space space... left parenthesis 2 right parenthesis

Solving (1) and (2), we get

straight R equals 5 over 2 space cm straight r space equals space 2 space cm

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Probability

The difference between outside and inside surface of a cylindrical metallic pipe 14 cm long is 44 cm². If the pipe is made of 99 cm³ of metal, find the outer and inner radii of the pipe.

Some More Questions From Probability Chapter

A table cover 4 m x 2 m is spread on a table. Find the cost of polishing the top of the table at र40 per square metre of 25 cm table cover is hanging all round the table.

A classroom is 7 m long, 6.5 m wide and 4 m high. It has one door 3 m x 1.4 m and three windows each measuring 2 m x 1 m. The interior wall is to be colour washed. Find the cost of colour washing at the rate of र 3.50 per m².

Two cubes of side 6 cm each, are joined end to end. Find the surface area of the resulting cuboid.

The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rates of र 8 and र 9.50 per m² is र1248. Find the dimensions of the box.

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

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For Daily Free Study Material Join wiredfaculty

Probability

The difference between outside and inside surface of a cylindrical metallic pipe 14 cm long is 44 cm2. If the pipe is made of 99 cm3 of metal, find the outer and inner radii of the pipe.

Some More Questions From Probability Chapter

A table cover 4 m x 2 m is spread on a table. Find the cost of polishing the top of the table at र40 per square metre of 25 cm table cover is hanging all round the table.

A classroom is 7 m long, 6.5 m wide and 4 m high. It has one door 3 m x 1.4 m and three windows each measuring 2 m x 1 m. The interior wall is to be colour washed. Find the cost of colour washing at the rate of र 3.50 per m2.

Two cubes of side 6 cm each, are joined end to end. Find the surface area of the resulting cuboid.

The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rates of र 8 and र 9.50 per m2 is र1248. Find the dimensions of the box.

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The difference between outside and inside surface of a cylindrical metallic pipe 14 cm long is 44 cm². If the pipe is made of 99 cm³ of metal, find the outer and inner radii of the pipe.

A classroom is 7 m long, 6.5 m wide and 4 m high. It has one door 3 m x 1.4 m and three windows each measuring 2 m x 1 m. The interior wall is to be colour washed. Find the cost of colour washing at the rate of र 3.50 per m².

The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rates of र 8 and र 9.50 per m² is र1248. Find the dimensions of the box.