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?
 
please someone help me

Answer 1

PART A

Break up the barn into smaller shapes to find the area of each and then add them together to find the total surface area that he is going to be painting.

Two triangles of height = 4' and base = 20'

A=1/2 (b*h)

Area = 2 × (0.5×4×20) = 80

Two rectangles of length = 20' and width = 15'

Area= L*W

Area = 2 × 20 × 15 = 600

Two rectangles of length = 45' and width = 15'

Area= L*W

Area = 2 × 45' × 15' = 1350

Two rectangles on each on one side of the roof. We have the length = 45' but not the width. We can work out the width by using Pythagoras theorem

w² = 4² + 10²

w² = 16 + 100

w² = 116

w = √116 = 10.77

Area of the two rectangles on the roof part is = 2 ×10.77 × 45 = 969.33

Total area to paint = 969.33+1350+600+80 = 2999.33 (to the nearest hundredth)

Keep in mind that you are not painting the floor so there would be no need to add in the area of the base which is the floor.

PART B

Numbers of paint cans needed = 2999.33 ÷ 57 = 52.6 ≈ 53 cans

PART C

Total cost of paint = 53 × 23.50 = $1245.50

PART D

The barn is constructed by a cuboid and a rectangular prism

V of cuboid = length × width × height

V of cuboid = 20 × 45 × 15

V of cuboid = 13500

V of triangular prism = Area of cross section × depth

V = [0.5×4×20] × 45

V = 1800

Total volume = 1800 + 13500 = 15300