Question

Ralph is painting the barn below, including the sides and roof. He wants to know how much paint to purchase.

a.
What is the total surface area that he is going to be painting? Round your answer to the nearest hundredth.
b.
If one paint can covers 57 square feet, how many paint cans should he purchase?
c.
If each paint can costs $23.50, how much will the paint cost?
d.
Once the barn is finished being painted, there is going to be a party. Ralph wants to know how many people to invite to the party. What is the volume of the inside of the barn?

Answer 1

a. In the given figure,

The triangular prism is placed above a cuboid,

`\because √(4^2+10^2)=√(16+100)=√(116)`

∴ Surface area of the triangular prism,

`A_1= 2* (1)/(2)* 20* 4+2* √(116)* 45`

`=(80 + 90√(116))\text{ square feet}`

Now, the surface of the cuboid having dimensions 20' × 45' × 15'

So, the surface area of the cuboid,

`A_2=2* 20* 15 + 2* 45* 15`

`=1950\text{ square feet}`

Hence, the total surface area of the house,

`A=A_1+A_2`

`=80+90√(116)+1950`

`=2999.32966528`

`\approx 2999.33\text{ square feet}`

b. ∵ 1 paint = 57 square feet,

⇒ 1 square feet =
`(1)/(57)` paints,

⇒ The number of cans required for 2999.33 square feet =
`(2999.33)/(57)` ≈ 53

c. Since, the cost of one can = $ 23.50,

So, the cost of 53 cans = $ 1245.5,

d. The volume inside the barn = Volume of triangular prism + volume of cuboid

= 1/2 × 20 × 4 × 45 + 20 × 45 × 15

= 15,300 cube feet.