Question

The volume of a cube is given by the expression V=m^3 where (V) is the volume and (m) is the length of each side of the cube.The surface area of the cube is six times the product of (m) and (m). If the length of each side of the cube measure 3/4cm,what are the volume and the surface area of the cube? WRITE TO EXPLAIN YOUR THINKING

Answer 1

The volume is 27/64 cm^3

The surface area is 27/8 cm^2

Explanation:

We have the formula to calculate the volume is the following:

`\begin{gathered} V=m^3 \\ \\ \end{gathered}`

The value of m is 3/4

Replacing:

`\begin{gathered} V=\mleft((3)/(4)\mright)^3 \\ V=(3^3)/(4^3)=(27)/(64) \end{gathered}`

Now, for the surface area of cube is:

`A=6\cdot m^2`

Replacing:

`\begin{gathered} A=6\cdot\mleft((3)/(4)\mright)^2 \\ A=6\cdot(3^2)/(4^2)=6\cdot(9)/(16) \\ A=(54)/(16)=(27)/(8) \end{gathered}`