Question

A cylinder has a surface area of 360$\pi$ units square, and is 3 units tall. What is the diameter of the cylinder's circular base ?

• A. $24$ units
• B. $36$ units
• C. $32$ units
• D. $18$ units

Answer 1

The correct option is A $24$ units

The surface area of a cylinder is the area of the circular top and bottom, plus the area of its wrapped-around rectangular third face. You can express this in formula form as:

$SA=2\left(\pi r^2\right)+2\pi rh$

Substitute the known values into this formula to find the radius of the circular base:

$360\pi =2\left(\pi r^2\right)+2\pi r\left(3\right)$

$360\pi =2\pi r^2+6\pi r$

$r^2+3r-180=0$

$(r+15)(r-12)=0$

$r+15=0$ OR $r-12=0$

$r=-15,12$

Use only the positive value of r: 12. If r = 12, the diameter of the cylinder's circular base is 24.