Q. 10 - Geometry

Question

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

$\begin{array}{cc}e& \\ T.A.& \\ V& 64\end{array}$

$\begin{array}{cc}e& \\ T.A.& \\ V& 64\end{array}$

Step-by-Step Solution

Answer

$\begin{array}{cc}e& 4\\ T.A.& 96\\ V& 64\end{array}$

Step 1. Given information.

The volume of the cube is 64. That is$V=64$,$V=64$

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.

Firstly, find the length of edge of the cube using volume.

$\begin{array}{c}\text{V}=e^3\\ 64=e^3\\ 4\times 4\times 4=e^3\\ e=4\text{\hspace{0.17em}\hspace{0.17em}unit}\end{array}$

 

Then, the total area is given by:

$\begin{array}{c}\text{T.A.}=6e^2\\ =6{\left(4\right)}^2\\ =6\left(16\right)\\ =96{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$