Question

1. trash cans a cylindrical trash can is 30 inches high and has a base radius of 7 inches. a manufacturer wants to know the surface area of this trash can, including the top of the lid. what is the surface area? round to the nearest square inch.

Explanation:

Step1: Calculate the area of the two circular bases

The formula for the area of a circle is \(A = \pi r^{2}\). Given \(r = 7\) inches.
For two bases, \(A_{bases}=2\times\pi r^{2}=2\times\pi\times7^{2}=2\times\pi\times49 = 98\pi\)

Step2: Calculate the lateral (curved) surface area

The formula for the lateral surface area of a cylinder is \(A_{lateral}=2\pi r h\). Here \(r = 7\) inches and \(h = 30\) inches.
\(A_{lateral}=2\pi\times7\times30=420\pi\)

Step3: Calculate the total surface area

The total surface area \(A = A_{bases}+A_{lateral}\)
\(A=98\pi + 420\pi=518\pi\)
Substitute \(\pi\approx3.14\)
\(A = 518\times3.14=1626.52\)

Answer:

\(1627\) square inches (rounded to the nearest square inch)