Question

a small cube has the volume shown. its side length is 1.5 in. less than a second, larger cube. what is the volume of the larger cube?
volume: 87 in³
the volume of the larger cube is about \\(\square\\) in³
(do not round until the final answer. then round to the nearest whole number as needed.)
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Explanation:

Step1: Find small cube side length

The volume of a cube is $V = s^3$, so solve for $s$:
$$s = \sqrt[3]{V} = \sqrt[3]{87}$$
Calculate $\sqrt[3]{87} \approx 4.431$ in

Step2: Find large cube side length

Add 1.5 in to small cube side:
$$S = 4.431 + 1.5 = 5.931$$ in

Step3: Calculate large cube volume

Use $V_{large} = S^3$:
$$V_{large} = (5.931)^3 \approx 5.931 \times 5.931 \times 5.931$$
$$5.931^2 \approx 35.177, \quad 35.177 \times 5.931 \approx 208.6$$

Answer:

209