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Launch realize. 8-2: Find Volume of Cylinders (LMS graded)
8.2.PS-13
The cylinder shown has a volume of 824 cubic inches.
a. What is the radius of the cylinder? Use 3.14 for .
b. If the height of the cylinder is changed, but the volume
stays the same, then how will the radius change? Explain.
a. The radius of the cylinder is about 8.2 in³.
(Type an integer or decimal rounded to the nearest tenth as needed.)
10.7 in.
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Answer 1

To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the volume is 824 cubic inches, we can rearrange the formula to solve for the radius:

824 = πr²h

Since the height is not given, we cannot find the exact radius. However, we can still determine the relationship between the height and radius if the volume remains the same.

b. If the height of the cylinder is changed, but the volume stays the same, the radius will change inversely proportional to the height. This means that as the height increases, the radius will decrease, and vice versa. This relationship ensures that the volume remains constant.

Therefore, we cannot determine the exact radius without knowing the height, but we can conclude that the radius and height have an inverse relationship.