Question
29. Short Responss The smallest canister in a set of cylindrical canisters has a height of 11 inches and a radius of 1.5 inches. Round each answer to the nearest tenth. a. Find the volume of the smallest canister. b. The medium canister has the same height as the smallest but the radius is tripled. What is the volume of the medium canister?
Ask by Sanders Allan. in the United States
Feb 25,2025
Upstudy AI Solution
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Answer
a. The volume of the smallest canister is approximately 77.8 cubic inches.
b. The volume of the medium canister is approximately 699.3 cubic inches.
Solution
a. The volume of a cylinder is given by V = πr²h. For the smallest canister, r = 1.5 inches and h = 11 inches.
Volume = π × (1.5)² × 11 = π × 2.25 × 11 = 24.75π ≈ 77.8 cubic inches (rounded to the nearest tenth).
b. For the medium canister, the height remains 11 inches and the radius is tripled to 4.5 inches.
Volume = π × (4.5)² × 11 = π × 20.25 × 11 = 222.75π ≈ 699.3 cubic inches (rounded to the nearest tenth).
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Simplify this solution Bonus Knowledge
To find the volume of a cylinder, the formula is V = πr²h, where V is the volume, r is the radius, and h is the height. a. For the smallest canister: Volume = π(1.5)²(11) ≈ 78.5 cubic inches when rounded to the nearest tenth. b. The medium canister has a radius of 1.5 * 3 = 4.5 inches. Volume = π(4.5)²(11) ≈ 63.6 cubic inches when rounded to the nearest tenth.
