Question

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

$\begin{array}{cc}l& \\ w& 8\\ h& 5\\ \text{L.A.}& \\ \text{T.A.}& \\ V& 360\end{array}$

Short answer

\begin{align} l & = 9\\w &= 8\\ h&=5\\L.A.&=170\\T.A. &= 314\\V&=360\end{align}

Step-by-step solution

Step 1. Given information.

The width and height of a rectangle are 8 and 5 respectively. And the volume is 360.

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.

$\begin{array}{c}360=l\times 8\times 5\\ 360=l\times 40\\ l=\frac{360}{40}\\ l=9\text{\hspace{0.17em}\hspace{0.17em}unit}\end{array}$

Now.

$\begin{array}{c}\text{L.A.}=2(l+w)\times h\\ =2(9+8)\times 5\\ =2\left(17\right)\times 5\\ =34\times 5\\ =170{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

And

$\begin{array}{c}\text{T.A.}=72\text{+}2(9\times 8)\\ =72\text{+}2\left(72\right)\\ =72\text{+144}\\ =216{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$