Probability

Question

The volumes of two spheres are in the ratio 64 : 27. Find the difference of their surface areas, if the sum of their radii is 7 cm.

Solution

Let the radii of the two spheres be r¹ cm and r₂ cm respectively. Then,

straight v subscript 1 over straight v subscript 2 equals fraction numerator begin display style 4 over 3 end style πr subscript 1 cubed over denominator begin display style 4 over 3 end style πr subscript 2 cubed end fraction equals 64 over 27 rightwards double arrow space space open parentheses r subscript 1 over r subscript 2 close parentheses cubed equals open parentheses 4 over 3 close parentheses cubed rightwards double arrow space space space r subscript 1 over r subscript 2 equals 4 over 3 space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis straight r subscript 1 plus straight r subscript 2 equals 7 space cm space space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis

From (1) and (2)

straight r subscript 1 space equals space 4 space cm straight r subscript 2 space equals space 3 space cm

therefore

Difference of their surface areas
_{$equals 4 πr subscript 1 squared minus 4 πr subscript 2 squared equals space 4 πr left parenthesis straight r subscript 1 squared minus straight r subscript 2 squared right parenthesis equals space 4 straight pi space left parenthesis 4 squared minus 3 squared right parenthesis equals space 4 straight pi left parenthesis 16 minus 9 right parenthesis equals 4.22 over 7.7 equals space 88 space cm squared$}

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.

Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it (see figure). She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm, 40 cm and 20 cm respectively how many square sheets of paper of side 40 cm would she require?

Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm (see figure). Find how much he would spend for the tiles, if the cost of the tiles is र 360 per dozen.

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Probability

The volumes of two spheres are in the ratio 64 : 27. Find the difference of their surface areas, if the sum of their radii is 7 cm.

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.

Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm (see figure). Find how much he would spend for the tiles, if the cost of the tiles is र 360 per dozen.

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For Daily Free Study Material Join wiredfaculty

Probability

The volumes of two spheres are in the ratio 64 : 27. Find the difference of their surface areas, if the sum of their radii is 7 cm.

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.

Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm (see figure). Find how much he would spend for the tiles, if the cost of the tiles is र 360 per dozen.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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.