Question

A sphere of diameter 12.6 cm is melted and cast into a right circular cone of height 25.2 cm. Then the diameter of the base of the cone is :

• A. $6\text{cm}$
• B. $6.3\text{cm}$
• C. $12\text{cm}$
• D. $12.6\text{cm}$

Answer 1

Answer: (D)

$12.6\text{cm}$

Here $r=\frac{12.6}{2}=6.3\text{cm}$
Volume of the sphere $=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times \frac{22}{7}\times 6.3\times 6.3\times 6.3$

Volume of a cone $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times \frac{22}{7}\times 25.2\times r^2$
From the given data, we can understand that

Volume of the sphere = Volume of cone
$\Rightarrow \frac{4}{3}\times \frac{22}{7}\times 6.3\times 6.3\times 6.3=\frac{1}{3}\times \frac{22}{7}\times 25.2\times r^2$
$\Rightarrow r^2=6.3\times 6.3$
$\therefore r=6.3\text{cm}$
Diameter $=12.6\text{cm}$