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: 84 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.)

Explanation:

Step1: Find small cube side length

The volume of a cube is $V = s^3$, so solve for $s$:
$$s = \sqrt[3]{V} = \sqrt[3]{84}$$
Calculate $\sqrt[3]{84} \approx 4.3795$ in

Step2: Find larger cube side length

Add 1.5 in to small cube's side:
$$S = 4.3795 + 1.5 = 5.8795$$ in

Step3: Calculate larger cube volume

Use $V_{large} = S^3$:
$$V_{large} = (5.8795)^3 \approx 5.8795 \times 5.8795 \times 5.8795 \approx 203.9$$

Step4: Round to nearest whole number

Round 203.9 to the nearest integer:
$$203.9 \approx 204$$

Answer:

204