Question

Can someone help me ? Show steps please.

Answer 1

Answer:

C) 101.5 pi in^2

Step-by-step explanation:

A cylinder's area is found by next formula:

$A_T=A_B+A_L\\ A_T=2\pi r^2 +(2\pi r)h\\A_T=2\pi \left(r^2 + r h\right)$

This is because the cylinder has two circle bases and its lateral area is a rectangle whose base is the perimeter of a circle and whose height is the cylinder's height. My last step was to take the common factor.

From the figure you get the cylinder's height and the base diameter's length, which is double of radius'. Since we need "r":

$r=d/2=7/2\;\Longrightarrow r=3.5\;in$

Now, we replace height and radius in the formula:

$A_T=2\pi \left(r^2 + r h\right)\\A_T=2\pi \left(3.5^2 + 3.5\cdot 11\right)\\A_T=2\pi (50.75)\\\boxed{A_T=101.5\;in^2}$