Question

rash 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. in²

Explanation:

Step1: Find lateral - surface area formula

The formula for the lateral - surface area of a cylinder is $A_{l}=2\pi rh$, where $r$ is the radius and $h$ is the height. Given $r = 7$ inches and $h = 30$ inches, $A_{l}=2\pi\times7\times30=420\pi$ square inches.

Step2: Find area of two bases formula

The formula for the area of a circle is $A_{b}=\pi r^{2}$. Since there are two bases (top and bottom), $A_{2b}=2\pi r^{2}$. Substituting $r = 7$ inches, we get $A_{2b}=2\pi\times7^{2}=2\pi\times49 = 98\pi$ square inches.

Step3: Calculate total surface area

The total surface area $A$ of the cylinder is the sum of the lateral - surface area and the area of the two bases, $A=A_{l}+A_{2b}=420\pi+98\pi=518\pi$ square inches.

Step4: Approximate the value

Using $\pi\approx3.14$, $A = 518\times3.14=1626.52\approx1627$ square inches.

Answer:

$1627$