Answer :
: Estimate the volume: a) 15 in³, b) 32 in³, c) 72 in³, d) 81 in³. The estimated volumes are a) 15 in³, b) 32 in³, c) 72 in³, and d) 81 in³.
The volume of a cube is calculated using the formula V = s^3, where 's' represents the length of one side of the cube. To estimate the volume, we need to find the cube root of the given values.
a) For 15 in³: Cube root of 15 ≈ 2.466. Thus, the estimated side length of the cube is approximately 2.466 inches. Now, to find the volume, we cube this value: V ≈ 2.466³ ≈ 15 in³.
b) For 32 in³: Cube root of 32 ≈ 3.174. The estimated side length of the cube is approximately 3.174 inches. Calculating the volume: V ≈ 3.174³ ≈ 32 in³.
c) For 72 in³: Cube root of 72 ≈ 4.160. The estimated side length of the cube is approximately 4.160 inches. Volume calculation: V ≈ 4.160³ ≈ 72 in³.
d) For 81 in³: Cube root of 81 ≈ 4.326. The estimated side length of the cube is approximately 4.326 inches. Volume calculation: V ≈ 4.326³ ≈ 81 in³.
The given statement “Estimate the volume: a) 15 in³, b) 32 in³, c) 72 in³, d) 81 in³.” is true because the estimated volumes for options a, b, c, and d have been calculated accurately using the cube root method.
