Question

if the cardboard tube of a toilet paper roll has a diameter of 3.08 in and is 4 in tall, what is the lateral surface area of the cardboard roll? the lateral surface area is (type an exact answer in terms ers or decimals for any numbers in the expression.)

Explanation:

Step1: Find the circumference of the base

The formula for the circumference of a circle is \(C = \pi d\). Given \(d = 3.08\) in, so \(C=\pi\times3.08 = 3.08\pi\) in.

Step2: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(S = Ch\) (where \(C\) is the circumference of the base and \(h\) is the height). Given \(h = 4\) in and \(C=3.08\pi\) in. Then \(S=3.08\pi\times4=12.32\pi\) \(in^{2}\).

Answer:

\(12.32\pi\) \(in^{2}\)