Question

problems 1–3: draw a cylinder.

1. label the radius 3 units and the height 10 units.
2. determine the area of the base. write your response in terms of π.
3. determine the volume of the cylinder. write your response in terms of π.

problems 4–6: containers a and b hold oatmeal. container a is a rectangular prism and container b is a cylinder.

1. the diameter of container b is 5 inches. what is its radius?
2. which container’s base has a larger area? explain your thinking.
3. which has a larger volume: container a or b? explain your thinking.
4. here is a cylinder with a radius of 4 feet and a height of 9 feet. what is the volume of the cylinder in cubic feet? round your answer to the nearest hundredth.

Explanation:

Step1: Identify base area formula

The base of a cylinder is a circle, area formula: $A = \pi r^2$

Step2: Substitute radius $r=3$

$A = \pi (3)^2 = 9\pi$
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Step3: Identify cylinder volume formula

Volume formula: $V = \text{Base Area} \times h$

Step4: Substitute base area and $h=10$

$V = 9\pi \times 10 = 90\pi$
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Step5: Relate radius and diameter

Radius = $\frac{\text{Diameter}}{2}$

Step6: Substitute diameter=5 in

$r = \frac{5}{2} = 2.5$ inches
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Step7: Calculate Container A base area

Rectangular base area: $6 \times 4 = 24$ square inches

Step8: Calculate Container B base area

Cylinder base area: $\pi (2.5)^2 = 6.25\pi \approx 19.63$ square inches

Step9: Compare the two areas

$24 > 19.63$, so Container A's base is larger
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Step10: Calculate Container A volume

Rectangular prism volume: $24 \times 10 = 240$ cubic inches

Step11: Calculate Container B volume

Cylinder volume: $6.25\pi \times 10 = 62.5\pi \approx 196.35$ cubic inches

Step12: Compare the two volumes

$240 > 196.35$, so Container A has larger volume
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Step13: Substitute $r=4, h=9$ into volume formula

$V = \pi (4)^2 \times 9 = 144\pi$

Step14: Compute and round to nearest hundredth

$144\pi \approx 144 \times 3.1416 \approx 452.39$

Answer:

1. (Drawing: A cylinder with radius labeled 3 units and height labeled 10 units)
2. $9\pi$ square units
3. $90\pi$ cubic units
4. 2.5 inches
5. Container A's base has a larger area. Container A's base area is 24 square inches, while Container B's base area is approximately 19.63 square inches, and 24 > 19.63.
6. Container A has a larger volume. Container A's volume is 240 cubic inches, while Container B's volume is approximately 196.35 cubic inches, and 240 > 196.35.
7. 452.39 cubic feet