Question

A metallic solid cone is melted and cast into a cylinder of the same base as that of the cone. If the height of the cylinder is $7cm$, what was the height of the cone?

• A. $20cm$
• B. $21cm$
• C. $22cm$
• D. $12cm$

Answer 1

The correct option is B $21cm$

When a solid of one shape is melted into another shape, the amount of volume remains the same.
Volume of cone $=$ Volume of cylinder

$\frac{1}{3}\pi r_1^2{h}_1=\pi r_2^2{h}_2$

$\Rightarrow \frac{1}{3}\times r^2\times h_1=r^2\times 7[r_1=r_2=r]$ as same base

$\Rightarrow h_1=7\times 3=21cm$

Therefore, height of cone is $21$ cm.