Each side length of Cube $A$ is $4 cm$ long.
Each side length of Cube $B$ is triple the side length of Cube $A$ .
How many times greater is the volume of Cube $B$ than that of Cube A?
1664 times 192 times
27 times 9 times

Answer

Expert–verified

Hide Steps

Answer

$27$ times greater.

Steps

Step 1 ：Let the side length of Cube A be $a$ and the side length of Cube B be $b$ . Given that $b = 3 a$ , and $a = 4$ cm.

Step 2 ：Calculate the volume of Cube A: $V_{A} = a^{3} = 4^{3} = 64$ cubic cm.

Step 3 ：Calculate the side length of Cube B: $b = 3 a = 3 (4) = 12$ cm.

Step 4 ：Calculate the volume of Cube B: $V_{B} = b^{3} = 12^{3} = 1728$ cubic cm.

Step 5 ：Find how many times greater the volume of Cube B is than that of Cube A: $\frac{V_{B}}{V_{A}} = \frac{1728}{64} = 27$ .

Step 6 ： $27$ times greater.