Question

a) If a cube has a volume of 3375 cubic centimeters, how would you write the length of one side as a power? b) If a cube has a volume of 1527 cubic centimeters, what is the length of the sides? Round your answer to two decimal places.

Answer 1

Given:

The volume of the cube is

`\begin{gathered} V1=3375cm^3 \\ V2=1527cm^3 \end{gathered}`

Required:

To find the side length of the cube.

Step-by-step explanation:

The formula for volume of the cube is

`V=a^3`

Where a is the side length.

(a)

`\begin{gathered} 3375=a^3 \\ \\ a=\sqrt[3]{3375} \\ \\ a=\sqrt[3]{15^3} \\ \\ a=(15^3)^{(1)/(3)} \\ \\ a=15cm \end{gathered}`

1(b)

`\begin{gathered} 1527=a^3 \\ \\ a=\sqrt[3]{1527} \\ \\ a=11.52cm \end{gathered}`

Final Answer:

(a) The side length is 15cm.

(b) The side length is 11.52cm.

`\begin{gathered} \sqrt[3]{8}=2 \\ \\ And \\ \\ \sqrt[3]{8}=\sqrt[3]{2^3} \\ \\ =(2^3)^{(1)/(3)} \\ \\ =2 \end{gathered}`