Q30. - Geometry

Question

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

1. What is the total area to be painted?
2. A gallon of a certain type paint will cover only $200f{t}^2$ of area for the first coat, but on the second coat a gallon of the same paint will cover $300f{t}^2.$  If the fence is to be given two coats of paint, how many gallons of paint should be bought? 

Step-by-Step Solution

Answer

1. The area to be painted is  $2640f{t}^2$
2. Total paint required is22  gallon.

Step 1. Given information.

 Length of the wooden fence$=6ft$

Height of the wooden ffence $=220ft$

Step 2. Concept Used.

If bis the length of the wooden fence and h is the height of the fence.

Then, the   area of the fence is $A=b\times h$

Step 3. Let’s calculate the area of the fence.

Put the value of length and height into the formula and find the area.

Area of the fence   :$\begin{array}{c}A=220\times 6\\ =1320f{t}^2\end{array}$

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

i.e.

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

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

 

In the first coat $200f{t}^2=1$

 gallon

Then,$2640f{t}^2=\left(\frac{2640}{200}\right)=13.2$

 gallon

In the second coat$300f{t}^2=1$

 gallon

Then,$2640f{t}^2=\left(\frac{2640}{300}\right)=8.8$

 gallon

Thus$=(13.2+8.8)=22$

Total paint gallon

 

Therefore, the area to be painted is$2640f{t}^2$ and total paint required is 22gallon.