Question

find the surface area of each figure. complete parts (a) and (b).
a. cube
the surface area of the cube is
(simplify your answer. type an exact answer, using radicals as needed.)
b. right circular cylinder
the surface area of the right circular cylinder is
(simplify your answer. type an exact answer, using radicals as needed. type an exact answer, using

Explanation:

Step1: Surface area formula for cube

The surface area formula for a cube is \(SA = 6s^{2}\), where \(s\) is the side - length of the cube. Given \(s = 10\) cm.

Step2: Calculate the surface area of the cube

Substitute \(s = 10\) into the formula: \(SA=6\times(10)^{2}\).
First, calculate \((10)^{2}=100\). Then \(6\times100 = 600\) \(cm^{2}\).

Step3: Surface area formula for right - circular cylinder

The surface area formula for a right - circular cylinder is \(SA = 2\pi r^{2}+2\pi rh\), where \(r\) is the radius and \(h\) is the height. Given \(r = 4\) cm and \(h = 22\) cm.

Step4: Calculate \(2\pi r^{2}\)

Substitute \(r = 4\) into \(2\pi r^{2}\): \(2\pi\times(4)^{2}=2\pi\times16 = 32\pi\).

Step5: Calculate \(2\pi rh\)

Substitute \(r = 4\) and \(h = 22\) into \(2\pi rh\): \(2\pi\times4\times22=176\pi\).

Step6: Calculate the surface area of the cylinder

Add the two results: \(SA=32\pi + 176\pi=(32 + 176)\pi=208\pi\) \(cm^{2}\).

Answer:

a. \(600\) \(cm^{2}\)
b. \(208\pi\) \(cm^{2}\)