Question

If the diameter of the base of a right circular cylinder is 20% greater than its height h, then its volume is equal to (in cubic units)

• A. $\pi h^3$
• B. $0.36\pi h^3$
• C. $36\pi h^2$
• D. $3.6\pi h^3$

Answer 1

The correct option is B $0.36\pi h^3$

Let r be the radius of the right circular cylinder.
∴ 2r = h + 20% of h (Given)
$\Rightarrow 2r=h+(\frac{20}{100}\times h)=\frac{6h}{5}$
$\Rightarrow r=\frac{3h}{5}$
$\therefore \text{Volume of right circular cylinder}=\pi r^{2}h$
$=\pi {\left(\frac{3h}{5}\right)}^2\times h$ [From (i)]
$=\frac{9}{25}\pi h^3$
$=0.36\pi h^3$
Hence, the correct answer is option (b).