Question

a right - circular cylinder has a radius of 6 inches and a height of 5 inches. decrease the height and radius by 10%. use the formulas v = πr²h and sa = 2πrh+2πr² to answer parts a through b below.
a. find the volume v and surface area sa of the original cylinder.
the volume is v = 565.49 cubic inches
(round to the nearest hundredth as needed.)
the surface area is sa = 414.69 square inches.
(round to the nearest hundredth as needed.)
b. find the volume v and surface area sa of the new cylinder.
the volume is v = 410.31

Explanation:

Step1: Calculate new radius and height

The original radius $r = 8$ inches and height $h=5$ inches. Decreasing by 10%, the new radius $r_{new}=r\times(1 - 0.1)=8\times0.9 = 7.2$ inches and new height $h_{new}=h\times(1 - 0.1)=5\times0.9 = 4.5$ inches.

Step2: Calculate volume of new - cylinder

The volume formula of a cylinder is $V=\pi r^{2}h$. Substitute $r = 7.2$ and $h = 4.5$ into the formula: $V=\pi\times(7.2)^{2}\times4.5=\pi\times51.84\times4.5\approx3.14\times51.84\times4.5 = 729\times0.5652=400.9488\approx400.95$ cubic inches.

Step3: Calculate surface - area of new cylinder

The surface - area formula of a cylinder is $SA = 2\pi rh+2\pi r^{2}$. Substitute $r = 7.2$ and $h = 4.5$ into the formula:

$$
LATEXBLOCK0
$$

Answer:

The volume is $V\approx400.95$ cubic inches.
The surface area is $SA\approx529.03$ square inches.