Questions: Find the surface area of a cylinder with a base diameter of 10 ft and a height of 7 ft. Write your answer in terms of π, and be sure to include the correct unit.

Find the surface area of a cylinder with a base diameter of 10 ft and a height of 7 ft. Write your answer in terms of π, and be sure to include the correct unit.

Transcript text: Find the surface area of a cylinder with a base diameter of 10 ft and a height of 7 ft. Write your answer in terms of $\pi$, and be sure to include the correct unit.

Solution

Solution Steps

Step 1: Calculate the area of the two circular bases

The area of one circular base is given by the formula $\pi r^2$. Since there are two bases, we multiply this area by 2: \[2\pi r^2 = 2\times3.14159\times5^2 = 157.08\]

Step 2: Calculate the area of the side of the cylinder

The area of the side can be thought of as the circumference of the base $2\pi r$ multiplied by the height $h$: \[2\pi rh = 2\times3.14159\times5\times7 = 219.91\]

Step 3: Calculate the total surface area of the cylinder

The total surface area $A$ is the sum of the area of the two bases and the area of the side: \[A = 2\pi r^2 + 2\pi rh = 157.08 + 219.91 = 376.99\]