Question

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

$\begin{array}{cc}l& 50\\ w& 30\\ h& 15\\ \text{L.A.}& \\ \text{T.A.}& \\ V& \end{array}$

Short answer

$\begin{array}{cc}l& 50\\ w& 30\\ h& 15\\ \text{L.A.}& 2400\\ \text{T.A.}& 5400\\ V& 22500\end{array}$

Step-by-step solution

Step 1. Given information.

The length, width and height of a rectangle are 50, 30 and 15 respectively.

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.

Now, substitute all the given values in the formula.

$\begin{array}{c}\text{L.A.}=2(l+w)\times h\\ =2(50+30)\times 15\\ =2\left(80\right)\times 15\\ =160\times 15\\ =2400{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

And

$\begin{array}{c}\text{T.A.}=2\text{400+}2(50\times 30)\\ =2\text{400+}2\left(1500\right)\\ =2\text{400+3000}\\ =5400{\text{\hspace{0.17em}\hspace{0.17em}unit}}^2\end{array}$

And the volume is

$\begin{array}{c}\text{V}=50\times 30\times 15\\ =1500\times 15\\ =22500{\text{\hspace{0.17em}\hspace{0.17em}unit}}^3\end{array}$