Question

A cone of height 36 cm and base radius 9 cm is reshaped into a sphere. Find the radius of the sphere formed.

• A. 9 cm
• B. 10 cm
• C. 8 cm
• D. 15 cm

Answer 1

The correct option is

D

9 cm

Volume of the cone = $\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi \times (9{)}^2\times 36$

Volume of a Sphere = $\frac{4}{3}\pi r^3$

Volume of the old solid = Volume of the new solid formed

$\Rightarrow$ $\frac{1}{3}\pi \times (9{)}^2\times 36=\frac{4}{3}\pi r^3$

$\Rightarrow$$(9{)}^2\times 9\times 4=4\times r^3$

= $r^3=(9{)}^3$

$⟹$ radius of sphere formed = 9