Q7. - Geometry

Question

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

$\begin{array}{cc}e& 3\\ T.A.& \\ V& \end{array}$

Step-by-Step Solution

Answer

$\begin{array}{cc}e& 3\\ T.A.& 54\\ V& 27\end{array}$

Step 1. Given information.

The length of the edge of the cube is 3. That is,$e=3$ .

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:

$\begin{array}{c}\text{T.A.}=6e^2\\ =6{\left(3\right)}^2\\ =6\left(9\right)\\ =54{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

And the volume is

$\begin{array}{c}\text{V}=e^3\\ ={\left(3\right)}^3\\ =3\times 3\times 3\\ =27{\text{\hspace{0.17em}\hspace{0.17em}unit}}^3\end{array}$