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 $6(2+3p)^2\ \text{cm}^2$.