Question

The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone of height 24 cm is made. Find the radius of its base.

Answer 1

The dimensions of the cuboid are 44 cm, 21 cm and 12 cm.

Let the radius of the cone be r cm.

Height of the cone, h = 24 cm

It is given that cuboid is melted to form a cone.

∴ Volume of metal in cone = Volume of metal in cuboid

= `1/3pir^2h = 44 xx 21 xx 12` (Volume of cuboid = Length × Breadth × Height)

\[ \Rightarrow \frac{1}{3} \times \frac{22}{7} \times r^2 \times 24 = 44 \times 21 \times 12\]

\[ \Rightarrow r = \sqrt{\frac{44 \times 21 \times 12 \times 21}{22 \times 24}} = \sqrt{21 \times 21} = 21 cm\]

Thus, the radius of the base of cone is 21 cm.