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?

a) 2899.33

b) 51

c) 1222

d) 14700

Step-by-step explanation:

a) Find out the area of all sides one by one and add it at the end

Area of triangle at front + Area of triangle at the back

Area of triangle = 1/2 x base x height + 1/2 x base x height

Area = 1/2 x 20 x 4 + 1/2 x 20 x 4

Area = 40 + 40

Area = 80

Area of rectangle at front + Area of rectangle at back

Area of rectangle = length x breadth + length x breadth

Area = 20 x 15 + 20 x 15

Area = 300 + 300

Area = 600

Area of rectangle on both sides

Area of rectangle = length x breadth x 2

Area = 45 x 15 x 2 = 1350

Area of rectangle at the bottom

Area of rectangle = length x breadth

Area = 45 x 20 = 900

Area of rectangle at both sides of the roof

Find the side length of the roof through the triangle

c² = a² + b²

c² = 4² + 10²

c = √116

c = 2√29

Area of rectangle = length x breadth x 2

Area = 45 x 2√29 x 2

Area = 969.33

Add all areas

Total surface area = 80 + 600 + 350 + 900 + 969.33

Total surface area = 2899.33

b)

1 paint can cover 57 square feet

x paints can cover 2899.33 square feet

1 : 57

x : 2899.33

Cross multiply

57x = 2899.33

x = 50.86 rounded off to 51

Therefore, 51 paint cans should be purchased to paint.

c)

1 paint costs $23.50

52 paints cost $x

1 : 23.5

52 : x

Cross multiply

x = 52 x 23.5

x = $1222

Therefore, the paint will cost $1222.

d)

Volume of cuboid = length x width x height

Volume = 20 x 45 x 15

Volume = 13500

Volume of pyramid = 1/3 x Base Area x Height

Volume = 1/3 x (20 x 45) x 4

Volume = 1200

Total Volume = 1200 + 13500

Total Volume = 14700

!!

34

step-by-step explanation:

8

step-by-step explanation: