Given two similar solid cylinders with volumes 4096 cm³ and 1728 cm³, find the height of the larger cylinder if the smaller cylinder has a height of 12 cm.

April 29, 2026Mathematics

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April 29, 2026

Answer

4096 cm^3 $$

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4. Similar Solid Cylinders and Composite Solid Volume

a) Find the height of the larger cylinder.

Step 1: Determine the ratio of the volumes of the two similar cylinders. Let $V_L$ be the volume of the larger cylinder and $V_S$ be the volume of the smaller cylinder. $V_L = 4096 cm^3$ $V_S = 1728 cm^3$ The ratio of volumes is: $\frac{V_L}{V_S} = \frac{4096}{1728}$ Simplify the ratio:

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You're on a roll — 4. Similar Solid Cylinders and Composite Solid Volume a) Find the height of the larger cylinder.

Asked on April 29, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 29, 2026

You're on a roll — 4. Similar Solid Cylinders and Composite Solid Volume a) Find the height of the larger cylinder. Step 1: Determine the ratio of the volumes of the two similar cylinders. Let V_L be the volume of the larger cylinder and V_S be the volume of the smaller cylinder. V_L = 4096 cm^3 V_S = 1728 cm^3 The ratio of volumes is: (V_L)/(V_S) = (4096)/(1728) Simplify the ratio: 409