Final answer:
To calculate the ratio of the side lengths of two cubes given their volumes, find the cube root of each volume and then form the ratio. The side length of Cube A is approximately 2 1 3 inches and that of Cube B is the cube root of 2. The closest whole number ratio of these side lengths is 3:2. So the correct answer is Option D.
Step-by-step explanation:
The question asks to find the ratio of the side lengths of two cubes given their volumes. Since the volume of a cube is the cube of its side length (V = s³), we can find the side length of each cube by taking the cube root of the volume. Cube A has a volume of 9 in³, so its side length (s) is the cube root of 9. Cube B has a volume of 2 in³, so its side length (s) is the cube root of 2. The ratio of the side lengths is therefore the ratio of these cube roots.
To find the cube root of 9, we know that 2³ = 8 and 3³ = 27, so the cube root of 9 is between 2 and 3, closer to 2. For precision, it is approximately 2.08, but for the ratio, we can consider it approximately 2 1 3. On the other hand, since the cube root of 2 is not a whole number, we'll refer to it as the cube root of 2 for the ratio, noting it's between 1 and 2 but closer to 1.
The closest answer choice that represents this ratio is (D) 3 : 2, since 2 1 3 is approximately 2 and the cube root of 2 is approximately 1(less than 2), making a simple ratio close to 3:2 when rounded to whole numbers.