Question

A cylinder of height 28 cm and radius 10 cm is melted and formed into 4 square base pyramids of equal volume. Find the height of the pyramid, if the length of its base is 20 cm.

Answer 1

ATQ,
Height of the cylinder $=28cm$.
Radius of the cylinder $=10cm$.
Now,
Volume of the cylinder$=\pi r^{2}h=\frac{22}{7}\times 10\times 10\times 28c{m}^3=8800c{m}^3$.
Now, the cylinder is melted and recast into $4$ pyramids of equal volumes.
So,
Volume of each pyramid $=\frac{8800}{4}c{m}^3=2200c{m}^3$.
As we know,
Volume of pyramid $=\frac{1}{3}\times a^2\times h$
Length of the base of pyramid $=20cm$
So,
$\Rightarrow \frac{1}{3}\times 20\times 20\times h=2200c{m}^3$
$\Rightarrow \frac{1}{3}\times 400\times h=2200c{m}^3$.
$\Rightarrow h=\frac{2200\times 3}{400}=16.5cm$.
Thus, height of the pyramid is $16.5cm$.