Question

Aina builds a cube model out of manila cards. If the volume of the constructed cube is (2+3p) ³ cm³, find the total surface area of the cube in terms of p.

HELPPPP

Answer 1

Given:

The volume of a cube =
`(2+3p)^3\ \text{cm}^3`

To find:

The total surface area of the cube in terms of p.

Solution:

Volume of a cube is:

`V=a^3` ...(i)

Where, a is the side length.

It is given that,

`V=(2+3p)^3\ \text{cm}^3` ...(ii)

On comparing (i) and (ii), we get

`a=2+3p\text{ cm}`

Now, the total surface area of a cube is:

`A=6a^2`

Where, a is the side length.

Putting
`a=2+3p`, we get

`A=6(2+3p)^2`

Therefore, the total surface area of the cube in terms of p is
`6(2+3p)^2\ \text{cm}^2`.