Question

Match the unknown $x$ for a cylinder with radius 'r ', height '2r' and volume 'V' (all measures in cm).

• A. 16π $c{m}^3$
• B. 54π $c{m}^3$
• C. 8 cm
• D. 3 cm

Answer 1

Given h = 2r,
Therefore, volume $V=\pi r^{2}h=\pi r^2\times 2r=2\pi r^3$

If h = 4 cm $\to$ r = 2 cm, $V=2\pi (2{)}^3=16\pi c{m}^3$

If r = 3 cm, h = 6 cm, $V=2\pi (3{)}^3=54\pi c{m}^3$

If $V=128\pi c{m}^3$, then $r^3=\frac{128\pi }{2\pi }$
$r^3=64=4^3$
r = 4 cm
So, h = 2r = 2 (4) = 8 cm.

If $V=54\pi c{m}^3\Rightarrow r^3=\frac{54\pi }{2\pi }$
$r^3=27=3^3$
r = 3 cm.