Question

If the curved surface area of a cylinder is $1760c{m}^2$ and its base radius is $14cm$, then its height is:

• A. $10cm$
• B. $20cm$
• C. $15cm$
• D. $40cm$

Answer 1

The correct option is B

$20cm$

Explanation for the correct option:

Find the height of the cylinder.

Given that, the curved surface area of the cylinder is $1760c{m}^2$

And, the radius $r$ of the cylinder $=14cm$

Let the height of the cylinder $=hcm$

The curved surface area of the cylinder of radius $r$ and height $h$ $=2\mathrm{\pi rh}$

$$\begin{gathered} \therefore 1760=2\times \frac{22}{7}\times 14\times h\left(\pi =\frac{22}{7}\right) \\ \Rightarrow 1760=2\times 22\times 2\times h \\ \Rightarrow h=\frac{1760}{2\times 22\times 2} \\ \Rightarrow h=\frac{1760}{88} \\ \Rightarrow h=20cm \end{gathered}$$

Hence, option (B) is the correct answer.