Chapter 11.1, Problem 30WE

(a)

To determine

To Find: The total area to be painted.

Answer to Problem 30WE

  $2640f{t}^2$

Explanation of Solution

Given: A wooden fence $6ft$ high and $220ft$ long is to be painted on both sides.

The area of the wooden fence

  $\begin{array}{l}A=bh\\ A=(220)(6)\\ A=1320f{t}^2\end{array}$

Since it is to be painted on both sides the painted area gets doubled

i.e.

  $\begin{array}{l}A=2\times 1320f{t}^2\\ A=2640f{t}^2\end{array}$

Hence, area to be painted is $2640f{t}^2$

(b)

To determine

To Find: How many gallon cans of paint should be bought?

Answer to Problem 30WE

  $22gallon$

Explanation of Solution

Given: A gallon of a certain type of paint will cover only $200f{t}^2$ of area of the first coat, but on the second coat of gallon of same paint will cover $300f{t}^2$ .If the fence is to be given two coats of paint.

Area to be painted is $2640f{t}^2$

In the first coat

  $200f{t}^2=1gallon$

Then

  $\begin{array}{l}2640f{t}^2=\left(\frac{2640}{200}\right)gallon\\ =13.2gallon\end{array}$

In the second coat

  $300f{t}^2=1gallon$

Then

  $\begin{array}{l}2640f{t}^2=\left(\frac{2640}{300}\right)gallon\\ =8.8gallon\end{array}$

Thus

Total paint

  $\begin{array}{l}13.2+8.8gallon\\ =22gallon\end{array}$

Hence, $22gallon$