Question

Question 6(Multiple Choice Worth 2 points)

(Surface Area of Cylinders MC)

Determine the exact surface area of the cylinder in terms of π.

cylinder with radius labeled 1 and three fourths centimeters and a height labeled 3 and one fourth centimeters

30 and three sixteenths times pi square centimeters
35 and seven eighths times pi square centimeters
11 and thirteen sixteenths times pi square centimeters
17 and one half times pi square centimeters
Question 7(Multiple Choice Worth 2 points)
(Surface Area of Cylinders MC)

A deli is trying out new labels for their cylindrical-shaped wheels of cheese. The label covers the entire wheel except the circular top and bottom.

If the wheel has a radius of 30 centimeters and a height of 20 centimeters, how many square centimeters of the wheel does the label cover? (Approximate using pi equals 22 over 7)

792,000 over 7 square centimeters
66,000 over 7 square centimeters
26,400 over 7 square centimeters
2,640 over 7 square centimeters

Answer 1

Answer: For Question 6:

The formula for the surface area of a cylinder is given by 2πrh + 2πr^2, where r is the radius and h is the height.

Plugging in the given values, we get:

Surface area = 2π(1.75)(3.25) + 2π(1.75)^2

Surface area = 11.5625π + 10.0625π

Surface area = 21.625π

Therefore, the exact surface area of the cylinder in terms of π is 21 and 13/16 times pi square centimeters. The closest option to this is option C.

For Question 7:

The label covers the entire surface area of the cylinder except the circular top and bottom. Therefore, the surface area of the label is equal to the lateral surface area of the cylinder.

The formula for the lateral surface area of a cylinder is given by 2πrh, where r is the radius and h is the height.

Plugging in the given values, we get:

Lateral surface area = 2π(30)(20)

Lateral surface area = 1200π

Approximating using π = 22/7, we get:

Lateral surface area ≈ 1200(22/7)

Lateral surface area ≈ 3,771.43

Therefore, the label covers approximately 3,771.43 square centimeters of the wheel. The closest option to this is option B, which is 66,000/7 square centimeters, or approximately 9428.57 square centimeters.

Explanation: