Q19 of 47 Page 1

A metallic solid sphere of radius 10.5 cm is melted and recasted into smaller solid cones, each of radius 3.5 cm and height 3 cm. How many cones will be made?

Given:

Radius of sphere, r = 10.5 cm


Radius of cone, R = 3.5 cm


Height of cone, H = 3 cm


Let a solid sphere be melted and recasted into n smaller solid cones.


So, volume of sphere = n (Volume of cones)


We know that volume of sphere = (4πr3)/3


And Volume of cone = πr2h/3


∴ (4πr3)/3 = n (πR2H/3)


⇒ (4π (10.5)3) / 3 = n (π (3.5)2 (3)) / 3


⇒ (4 (1157.625)) = n (36.75)


⇒ 4630.5 = n (36.75)


⇒ n = 4630.5 / 36.75


∴ n = 126


Ans. Number of cones made by melting a given solid sphere is 126.


More from this chapter

All 47 →
10

Draw a line segment of length 7 cm and divide it internally in the ratio 2: 3.

 18

If the mth term of an A. P. is 1/n and nth term is 1/m then show that its (mn)th term is 1.

 20

From the top of a 7 m high building, the angle of elevation of the top of a tower is 60° and the angle of depression of its foot is 45°. Find the height of the tower.

 28

Draw a right triangle in which the sides (other than the hypotenuse) are of lengths 4 cm and 3 cm. Now construct another triangle whose sides are 3/5 times the corresponding sides of the given triangle.