Question

The base of a cold drink can have an area of $25\pi {\text{cm}}^2$ and it has a height of $10\text{cm.}$ What is the curved surface area of the cold drink can?

• A. $50\pi {\text{cm}}^2$
• B. $10\pi {\text{cm}}^2$
• C. $200\pi {\text{cm}}^2$
• D. $100\pi {\text{cm}}^2$

Answer 1

The correct option is D $100\pi {\text{cm}}^2$

Given, area of the base $=25\pi {\text{cm}}^2$ and height of the can$\left(h\right)=10\text{cm}$
Let, the radius of the cold drink can is $r$

Area of the base $=\pi r^2$
$\Rightarrow 25\pi =\pi r^2(\text{given)}$
Divide both sides by $\pi$
$\Rightarrow \frac{25\pi }{\pi }=\frac{\pi r^2}{\pi }$
$\Rightarrow 25=r^2$
Taking square root both sides
$\Rightarrow \sqrt{25}=\sqrt{r^2}$
$\Rightarrow r=\pm 5$
$\Rightarrow r=5(\because \text{Radius of a cylinder can not be negative}\therefore r=-5\text{is rejected)}$

The curved surface area of the cylinder $=2\pi rh$
$=2\pi \times 5\times 10$
$=2\pi \times 50$
$=100\pi {\text{cm}}^2$

Option (d.) is the correct choice.