Question

A water tank can hold $2\pi {\text{m}}^3$ of water. If the radius of the tank is $1\text{m},$ then:

• A. height of the tank is $1\text{m}$
• B. height of the tank is $2\text{m}$
• C. curved surface area of the tank is $6\pi {\text{m}}^2$
• D. curved surface area of the tank is $4\pi {\text{m}}^2$

Answer 1

Answer: (B), (D)

curved surface area of the tank is $4\pi {\text{m}}^2$

Given, volume of the water tank $=2\pi {\text{m}}^3$ and radius of the tank$\left(r\right)=1\text{m}$

Step 1: Let the height of the tank can be $h$

Volume of the tank $=\pi r^{2}h$
$\Rightarrow 2\pi =\pi r^{2}h(\text{given)}$
$\Rightarrow 2\pi =\pi \times (1{)}^2\times h$
$\Rightarrow 2\pi =\pi h$
Divide both sides by $\pi$
$\Rightarrow \frac{2\pi }{\pi }=\frac{\pi h}{\pi }$
$\Rightarrow 2=h$
$\Rightarrow h=2$

Step 2: The curved surface area of the cylinder
$=2\pi rh$
$=2\pi \times 1\times 2$
$=2\pi \times 2$
$=4\pi {\text{m}}^2$
Options (b.) and (d.) are correct choices.