Question

The base of a soda can has an area of $25\pi$ square centimeters and a height of 10 centimeters. What is the surface area of the curved side of the can?

• A. $50\pi$ sq cm
  
• B. $100\pi$ sq cm
• C. $75\pi$ sq cm
• D. $150\pi$ sq cm

Answer 1

The correct option is B $100\pi$ sq cm

Given, the area of the base is 25π sq cm and the height of the can (h) is 10 cm.
Let the radius of the can be r.
Area of the base $=\pi r^2$
$\Rightarrow 25\pi =\pi r^2$
$\Rightarrow 25=r^2$
$\Rightarrow r=\sqrt{25}=5cm$ (The radius of the base of a cylinder cannot be negative.)

Area of the curved surface of the can $=2\pi rh$
$=2\pi \times 5\times 10=100\pi$ sq cm