Question

A glass is in the shape of a cylinder whose height is 4 times the radius. If the volume of the glass is 256π $f{t}^3$, then find the height of the cylinder.

• A. 18 ft
• B. 16 ft
• C. 8 ft
• D. 6 ft

Answer 1

The correct option is B 16 ft

Given, height (h) is 4 times the radius (r).

$\Rightarrow h=4r$

$\Rightarrow r=\frac{h}{4}$

We know that volume of a cylinder = $\pi r^{2}h$

Therefore, the volume of glass = $\pi r^{2}h=256\pi$

$\Rightarrow \pi \times (\frac{h}{4}{)}^2\times h=256\pi$

$\Rightarrow \frac{\pi h^3}{16}=16\times 16\pi$

$\Rightarrow h^3=16\times 16\times 16$

$\text{So, h}=16ft.$