Cube A has a volume of a cubic inches. If each side of Cube B is twice as long as each side of Cube A, then what is the

[BTGmoderatorDC]

Cube A has a volume of a cubic inches. If each side of Cube B is twice as long as each side of Cube A, then what is the volume of Cube B?

A. 2a
B. 4a
C. 6a
D. 8a
E. 16a


OA D

Source: Veritas Prep

[swerve]

Cube A has a volume of a cubic inches. If each side of Cube B is twice as long as each side of Cube A, then what is the volume of Cube B?

A. 2a
B. 4a
C. 6a
D. 8a
E. 16a


OA D

Source: Veritas Prep

We know that,

Volume of cube\(= L^3\)

Volume of cube \(A= a\) cubic inches
\(a= L^3\)
\(L= a^{1/3}\)

Side of cube \(B\) is twice as long as side of \(A\).
Side of Cube \(B= l= 2\cdot a^{1/3}\)

Volume of Cube \(B= l^3\)
\(= 2^3 \cdot \left(a^{1/3}\right)^3\)
\(=8\cdot a\)

[Scott@TargetTestPrep]

Cube A has a volume of a cubic inches. If each side of Cube B is twice as long as each side of Cube A, then what is the volume of Cube B?

A. 2a
B. 4a
C. 6a
D. 8a
E. 16a


OA D

Solution:

We can let the side of cube A = x and the side of cube B = 2x. Since the volume of cube A is a, we have x^3 = a. Then, the volume of cube B is (2x)^3 = 8x^3. Substituting a for x^3, we obtain 8a for the volume of cube B.

Alternate Solution:

Alternately, we can let the side of cube A = 1, and so each side of cube B = 2. The volume of cube A is 1 x 1 x 1 = 1, and the volume of cube B is 2 x 2 x 2 = 8. Thus, the volume of cube B is 8 times the volume of cube A. The volume of cube A was given as a, and so the volume of cube B will be 8a.

Answer: D