Q6. - Geometry

Question

Refer to rectangular solids with dimensions l, w and h. Complete the following table.

$\begin{array}{cc}l& 9\\ w& \\ h& 2\\ \text{L.A.}& 60\\ \text{T.A.}& \\ V& \end{array}$

Step-by-Step Solution

Answer

$\begin{array}{cc}l& 9\\ w& 6\\ h& 2\\ \text{L.A.}& 60\\ \text{T.A.}& 168\\ V& 108\end{array}$

Step 1. Given information.

The length and height of a rectangle are 9 and 2 respectively. And the lateral area is 60.

Step 2. Write the concept.

The lateral area of the rectangle is given by:

$\text{L.A.}=\text{Perimeter}\times \text{Height}$

 

The total area of the rectangle is given by:

$\text{T.A.}=\text{L.A.+}2\left(\text{Base}\right)$

 

The volume of rectangle is given by:

$\text{V}=l\times w\times h$

Step 3. Determine the value.

Firstly, find the third dimension of the rectangle using the lateral area.

 $\begin{array}{c}\text{L.A.}=2(l+w)\times h\\ 60=2(9+w)\times 2\\ \frac{60}{2}=(18+2w)\\ 30=18+2w\end{array}$

Then,

$\begin{array}{c}30-18=2w\\ w=\frac{12}{2}\\ =6\text{\hspace{0.17em}\hspace{0.17em}unit}\end{array}$

 

Now,

$\begin{array}{c}\text{T.A.}=60\text{+}2(9\times 6)\\ =60\text{+}2\left(54\right)\\ =60\text{+108}\\ =168{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

 

And the volume is:

 

$\begin{array}{c}V=l\times w\times h\\ =9\times 6\times 2\\ =54\times 2\\ =108{\text{\hspace{0.17em}\hspace{0.17em}unit}}^3\end{array}$