Box $A$ has a volume of 48 cubic meters. Box $B$ is similar to Box A. To create Box B, Box A's dimensions were doubled. What is the volume of Box B?
A. $24 m^3$
B. $96 m^3$
C. $288 m^3$
D. $384 m^3$
Answer (1)
The volume of Box A is 48 m 3 .
The dimensions of Box B are twice the dimensions of Box A.
The volume of Box B is calculated as V B = 8 × V A .
The volume of Box B is 384 m 3 .
Explanation
Problem Analysis We are given that Box A has a volume of 48 cubic meters. Box B is similar to Box A, and its dimensions are doubled compared to Box A. We need to find the volume of Box B.
Setting up the problem Let V A be the volume of Box A and V B be the volume of Box B. Let the dimensions of Box A be l A , w A , and h A (length, width, and height). Then, V A = l A × w A × h A = 48 m 3 .
Since the dimensions of Box B are doubled, its dimensions are l B = 2 l A , w B = 2 w A , and h B = 2 h A . Therefore, the volume of Box B is: V B = l B × w B × h B = ( 2 l A ) × ( 2 w A ) × ( 2 h A )
Calculating Volume of Box B We can rewrite the volume of Box B as: V B = 2 × 2 × 2 × ( l A × w A × h A ) = 8 × ( l A × w A × h A ) = 8 × V A
Final Calculation Since V A = 48 m 3 , we can substitute this value into the equation for V B :
V B = 8 × 48 = 384 m 3
Conclusion Therefore, the volume of Box B is 384 cubic meters.
Examples
Imagine you're designing a storage container and realize you need a larger version that maintains the same proportions. If you double all the dimensions of your original container, the new container will have 8 times the volume. This principle is useful in scaling designs, whether for packaging, architecture, or even furniture, ensuring that the proportions remain consistent while adjusting the overall size and capacity.
