Q8 of 32 Page 267

A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter cm and height 3 cm. Find the number of cones so formed.


Given that, diameter(d) of sphere is 28 cm and diameter(D) of cone is and height(h) is 3 cm.


⇒ radius(r) of sphere


And, radius(R) of cone


⇒vol. of spheres



⇒ vol. of cone



⇒ vol. of sphere = n × vol. of 1 cone


(where, n is no. of cones)




⇒ n = 672


More from this chapter

All 32 →
4

A well of diameter 14 m. is dug 15 m. deep. The earth taken out of it has been spread evenly to form circular embankment of width 7 m. Find the height of the embankment.

 5

A container shaped like a right circular cylinder having diameter 12 cm. and height 15 cm. is full of ice cream. The ice-cream is to be filled into cones of height 12 cm. and diameter 6 cm., having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

 6

How many silver coins, 1.75 cm. in diameter and thickness 2 mm, need to be melted to form a cuboid of dimensions 5.5cm × 10cm × 3.5cm.?

 7

A vessel is in the form of an inverted cone. Its height is 8 cm. and the radius of its top is 5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, of the water flows out. Find the number of lead shots dropped into the vessel.