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 × 11 × 7 cm³

Let no. of cones formed = n

Now, according of question 

Volume of n cones = volume of cuboid

Number of cones formed are 24.

Answer 2

Let ‘n’ cones are formed

⇒ Volume of cuboid = n × volume of one cone

⇒ \(24\times 11 \times 7 = n \times \frac 13\times \pi \times (3.5)^2 \times 6\)

⇒ \(24\times 11 \times 7 = n \times \frac{22}7 \times 3.5 \times 3.5 \times 2\)

⇒ \(n = \frac{24 \times 11 \times 7}{22 \times 3.5}\)

⇒ n = 24 cones are formed.