Question

which is closest to the total surface area of a cylinder with a radius of 5 inches and a height that is equal to its diameter?
a 314 sq in.
b 471 sq in.
c 596 sq in.
d 785 sq in.
options: b, a, c, d

Explanation:

Step1: Find the height of the cylinder

The radius \( r = 5 \) inches. The diameter \( d = 2r = 10 \) inches. The height \( h \) is equal to the diameter, so \( h = 10 \) inches.

Step2: Recall the formula for the total surface area of a cylinder

The total surface area \( SA \) of a cylinder is given by \( SA = 2\pi r^2 + 2\pi rh \).

Step3: Substitute the values of \( r \) and \( h \) into the formula

First, calculate \( 2\pi r^2 \): \( 2\times\pi\times5^2 = 2\times\pi\times25 = 50\pi \).
Then, calculate \( 2\pi rh \): \( 2\times\pi\times5\times10 = 100\pi \).
Now, add these two parts together: \( SA = 50\pi + 100\pi = 150\pi \).

Step4: Approximate the value using \( \pi \approx 3.14 \)

\( 150\pi \approx 150\times3.14 = 471 \) square inches.

Answer:

B. 471 sq in.