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Probability

Question

Wired Faculty App

A spherical ball of lead 3 cm in radius is melted and recast into three spherical balls. If the radii of two balls are $3 over 2$ cm and 2 cm, find the diameter of the third ball.

Solution

Let the radius of the third ball be r cm. Then, according to the question,

4 over 3 straight pi left parenthesis 3 right parenthesis cubed equals 4 over 3 straight pi open parentheses 3 over 2 close parentheses cubed plus 4 over 3 straight pi left parenthesis 2 right parenthesis cubed plus 4 over 3 straight pi left parenthesis straight r right parenthesis cubed rightwards double arrow space space space 27 equals 27 over 8 plus 8 plus straight r cubed rightwards double arrow space space space straight r cubed equals 155 over 8 space rightwards double arrow space straight r equals fraction numerator square root of 155 over denominator 2 end fraction space cm rightwards double arrow space space space 2 straight r equals square root of 155 space cm

Hence, the diameter of the third ball is

square root of 155

cm.

Some More Questions From Probability Chapter

Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4 m × 3 m?

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?

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