Question

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

$\begin{array}{cc}l& 6\\ w& 3\\ h& \\ \text{L.A.}& \\ \text{T.A.}& \\ V& 54\end{array}$

Short answer

$\begin{array}{cc}l& 6\\ w& 3\\ h& 3\\ \text{L.A.}& 54\\ \text{T.A.}& 90\\ V& 54\end{array}$

Step-by-step solution

Step 1. Given information.

The length and width of a rectangle are 6 and 3 respectively. And the volume is 54.

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 volume.

$\begin{array}{c}54=6\times 3\times h\\ 54=18\times h\\ h=\frac{54}{18}\\ h=3\text{\hspace{0.17em}\hspace{0.17em}unit}\end{array}$

Now.

$\begin{array}{c}\text{L.A.}=2(l+w)\times h\\ =2(6+3)\times 3\\ =2\left(9\right)\times 3\\ =18\times 3\\ =54{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

And

$\begin{array}{c}\text{T.A.}=54\text{+}2(6\times 3)\\ =54\text{+}2\left(18\right)\\ =54\text{+36}\\ =90{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$