Question

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

• A. $15.75m$
• B. $12.6cm$
• C. $39.69cm$
• D. $69.39cm$

Answer 1

The correct option is B $12.6cm$

Given:

$\Rightarrow$ diameter of sphere$\left(d\right)=12.6cm$

$\Rightarrow$ radius $\left(r_1\right)=\frac{d}{2}=6.3cm$

$\Rightarrow$ height of the cone$=25.2cm$

Let radius of the cone $=r$

Volume of sphere $\left(V_s\right)$ $=$ volume of cone $\left(V_c\right)$

$\Rightarrow$ $\frac{4}{3}\pi (r_1{)}^3=\frac{1}{3}\pi (r^2)\times h$

$\Rightarrow$ $\frac{4}{3}\pi (6.3{)}^3=\frac{1}{3}\pi (r^2)\times 25.2$

$\Rightarrow$ $r^2=\frac{4\times 6.3\times (6.3{)}^2}{25.2}$

$\Rightarrow$ $r=6.3$

Diameter $D=2r=12.6cm$