Q12. - Geometry

Question

Refer to cubes with edges of length e. Complete the following table.

$\begin{array}{cc}e& 2x\\ T.A.& \\ V& \end{array}$

Step-by-Step Solution

Answer

$\begin{array}{cc}e& 2x\\ T.A.& 24x^2\\ V& 8x^3\end{array}$

Step 1. Given information.

The length of the edge of the cube is 2x. That is,$e=2x$ .

Step 2. Write the concept.

The total area of the cube is given by:

$\text{T.A.}=6e^2$

 

The volume of rectangle is given by:

$\text{V}=e^3$

Step 3. Determine the value.

Now, substitute all the given values in the formula.

Then, the total area is given by:

$\begin{array}{c}\text{T.A.}=6e^2\\ =6{\left(2x\right)}^2\\ =6\left(4x^2\right)\\ =24x^2{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

And the volume is

$\begin{array}{c}\text{V}=e^3\\ ={\left(2x\right)}^3\\ =2x\times 2x\times 2x\\ =8x^3{\text{\hspace{0.17em}\hspace{0.17em}unit}}^3\end{array}$