Question

The circumference of the base of a right circular cylinder is 252 cm. Find the lateral surface area if the height is 3 m.​

Answer 1

Answer:

The lateral surface area is  $80,638.4 \ cm^2$

Step-by-step explanation:

Lateral Surface Area of a Cylinder

It can be computed with the formula:

$\displaystyle A=\pi r^2+2\pi rh$

Where:

r = radius of the circular base

h = height

The circumference of the base can be calculated as:

$C = 2\pi r$

We are given the circumference C=252 cm, let's find the radius solving for r:

$\displaystyle r=\frac{C}{2\pi}$

$\displaystyle r=\frac{252\ cm}{2\pi}$

r = 40.1 cm

Now we calculate the lateral surface area knowing h=3 m=300 cm:

$\displaystyle A=\pi 40.1^2+2\pi 40.1*300$

$\boxed{A = 80,638.4 \ cm^2}$

The lateral surface area is $80,638.4 \ cm^2$