Q11. - Geometry

Question

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

$\begin{array}{cc}e& \\ T.A.& 150\\ V& \end{array}$

$\begin{array}{cc}e& \\ T.A.& 150\\ V& \end{array}$

Step-by-Step Solution

Answer

$\begin{array}{cc}e& 5\\ T.A.& 150\\ V& 125\end{array}$

Step 1. Given information.

The total area of the cube is 150. That is,$\text{T.A.}=150$$\text{T.A.}=150$ .

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:

$\text{V}=e^3\text{V}=e^3$

Step 3. Determine the value.

Firstly, find the length of edge of the cube using total area.

$\begin{array}{c}\text{T.A.}=6e^2\\ 150=6e^2\\ \frac{150}{6}=e^2\end{array}$ 

So,

$\begin{array}{c}25=e^2\\ 5\times 5=e^2\\ e=5\text{\hspace{0.17em}\hspace{0.17em}unit}\end{array}$

 $\begin{array}{c}25=e^2\\ 5\times 5=e^2\\ e=5\text{\hspace{0.17em}\hspace{0.17em}unit}\end{array}$

Then, the volume is

width="89" style="max-width: none; vertical-align: -46px;" $\begin{array}{c}\text{V}=e^3\\ ={\left(5\right)}^3\\ =5\times 5\times 5\\ =125{\text{\hspace{0.17em}\hspace{0.17em}unit}}^3\end{array}$