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Q3.

Expert-verifiedFound in: Page 478

Book edition
Student Edition

Author(s)
Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages
227 pages

ISBN
9780395977279

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

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

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

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

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:

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

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

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

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