Question

a right - circular cylinder has a radius of 6 inches and a height of 6 inches. decrease the height and radius by 10%. use the formulas v = πr²h and sa = 2πrh+2πr² to answer parts a through d below.
a. find the volume v and surface area sa of the original cylinder.
the volume is v =
(round to the nearest
cubic inches.
inches.
square inches.

Explanation:

Step1: Calculate the volume of the original cylinder

Given the formula for the volume of a cylinder $V = \pi r^{2}h$, with $r = 6$ inches and $h = 6$ inches. Substitute the values: $V=\pi\times6^{2}\times6=\pi\times36\times6 = 216\pi$ cubic - inches. Rounding $\pi\approx3.14$, we get $V\approx216\times3.14 = 678.24$ cubic inches.

Step2: Calculate the surface - area of the original cylinder

The formula for the surface - area of a cylinder is $SA = 2\pi rh+2\pi r^{2}$. Substitute $r = 6$ inches and $h = 6$ inches. First, calculate $2\pi rh$: $2\pi\times6\times6 = 72\pi$. Then calculate $2\pi r^{2}$: $2\pi\times6^{2}=2\pi\times36 = 72\pi$. Then $SA=72\pi + 72\pi=144\pi$ square inches. Rounding $\pi\approx3.14$, we get $SA\approx144\times3.14 = 452.16$ square inches.

Answer:

The volume is $V\approx678.24$ cubic inches.
The surface - area is $SA\approx452.16$ square inches.