Question

Find the total surface area of a cylinder that has a radius of $7$ inches and a height of $3$ inches. (Assume $\pi =\frac{22}{7}$.)

• A. $330$ sq in
• B. $110$ sq in
• C. $220$ sq in
• D. $440$ sq in

Answer 1

The correct option is D $440$ sq in

Let’s unfold the cylinder.
The area of the cylinder is equal to the sum of the area of two circles and the area of the rectangle.

Total area of the cylinder $=2\times$ area of each circle + area of the rectangle

Area of each circle $=\pi r^2$
Area of the rectangle = length $\times$ width $=2\pi r\times h=2\pi rh$

Therefore, total area$=2\times \pi r^2+2\pi rh=2\pi r(r+h)$
Now $\pi =\frac{22}{7},r=7,$ and $h=3$.

Total area $=2\times \left(\frac{22}{7}\right)\times \left(7\right)\times (7+3)=44\times 10=440$ sq in