Question

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

Answer 1

Answer:

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

!!