Question

surface area and volume of cylinders
using a net
the net of a cylinder is shown. the area of one base of the cylinder is ( 9pi \text{ in.}^2 ). the circumference of a base is ( 6pi \text{ in.} ), and the height of the cylinder is 10 in. which expression can you use to find the lateral area plus two bases of the cylinder?
( 6pi + 9pi(10) \text{ in.}^2 )
( 9pi + 9pi + 6pi(10) \text{ in.}^2 )
( 6pi + 6pi + 9pi(10) \text{ in.}^2 )
( 9pi + 6pi(10) \text{ in.}^2 )

Explanation:

Step1: Recall the formula for the surface area of a cylinder

The surface area of a cylinder \(S = 2\pi r^{2}+2\pi rh\), where \(2\pi r^{2}\) is the area of two bases and \(2\pi rh\) is the lateral area. In terms of the given values, the area of one base \(A_{base}=\pi r^{2}=9\pi\), so the area of two bases is \(9\pi + 9\pi\). The lateral area \(A_{lateral}=Ch\) (where \(C\) is the circumference of the base and \(h\) is the height). Given \(C = 6\pi\) and \(h = 10\), the lateral area is \(6\pi\times10\).

Step2: Combine the areas

The total surface area (lateral area plus two bases) is the sum of the area of two bases and the lateral area. So, \(S=9\pi + 9\pi+6\pi\times10\)

Answer:

\(9\pi + 9\pi + 6\pi(10)\text{ in.}^2\)