Question

A solid metallic cuboid of dimension 24 cm × 11 cm × 7 cm is melted and recast into solid cones of base radius 3.5 cm and height 6 cm. Find the number of cones so formed.

Answer 1

Volume of cuboid = 24 cm × 11 cm × 7 cm³

Volume of 1 cone = `1/3 ≠r^2h`

= `1/3 xx 22/7 xx (3.5)^2 xx 6  cm^3`

Let no. of cones formed be n.

Now, according to the question,

Volume of n cones = Volume of cuboid

`n xx 1/3 xx 22/7 xx (3.5)^2 xx 6 = 24 xx 11 xx 7`

∴ `n = (24 xx 11 xx 7 xx 3 xx 7)/(22 xx 3.5 xx 3.5 xx 6)`

⇒ n = 24