Question

Colton is planning on building a new shed for his backyard. The plans for the shed are shown with all the measurements. The shed is a right prism.

• How much can Colton store inside the new shed? Explain your reasoning.
• Colton wants to paint the outside of the shed including the shed door to match his house.
Explain how much paint Colton will need to paint the shed.
• A gallon of paint covers 200 square feet and costs $16.99. How much will it cost Colton to
paint the shed?
Your work should include:
• An explanation using math terms of how you could determine how much Colton can store
inside his shed (3 points)
• An explanation using math terms of how much paint Colton will need to paint the shed
(3 points)
• Your calculations (3 points)
• Statement explaining how much it will cost to paint the shed (3 points)
5 ft
4 ft
8 ft
6 ft 12 ft

Answer 1

The answer would be 6ft and the reason why is because the shed

Answer 2

Colton can on store goods equivalent to the volume of the shed. Volume is the capacity to hold something. Capacity of the shed is 576 ft³.

The paints will cover the surface of the shed, therefore amount of paints needed depends on the surface area of the shed not the volume.

From the calculations it will cost around $24.45 to point the whole house.

How the value for volume and surface area of the shed is calculated.

Colton can on store goods equivalent to the volume of the shed. Volume is the capacity to hold something.

Let's calculate the volume

Volume = LxWxH

Dimensions of the house are

Length, L= 12 ft

Width, W=6 ft and Height, H = 8 ft.

Volume of the house

= L×W×H= 12×8×6= 576 ft³

The paints will cover the surface of the shed, therefore amount of paints needed depends on the surface area of the shed not the volume.

Let's calculate the total surface area of the shed

Area of the front side = 6×8 =48 ft²

Area of the right side=12×8=96 ft²

Area of back side= area of front side=48 ft²

Area of left side=area of right side=96 ft²

Total external surface area of the four walls= 2×(48+96)= 2×144 = 288 ft²

One gallon of paint covers 200 ft² surface.

Therefore number of gallons needed = 288/200= 1.44 gallons.

Rate per gallon= $16.99

So total amount to be paid for painting the external surface= $16.99×1.44 = $24.45

So, from the calculations it will cost around $24.45 to point the whole house.