Question

A cylinder with base radius of $8$cm and height of $2$cm is melted to form a cone of height $6$cm. The radius of the cone will be ________.

• A. $4$cm
• B. $5$cm
• C. $6$cm
• D. $8$cm

Answer 1

The correct option is D $8$cm

Let $V_1$ and $V_2$ are the volumes of cylinder and cone respectively.

Cylinder is melted to form a cone,

$\therefore V_1=V_2$

$\Rightarrow \pi \times 8^2\times 2=\frac{1}{3}\pi \times r^2\times 6$ (where r is the radius of cone)

$\Rightarrow r^2=8^2\Rightarrow r=8cm$