Question

area and volume
distinguishing between surface area and volume
e figure below shows a shed in the shape of a rectangular prism.
ote that the shed has a floor.
10 ft
12 ft
9 ft
(a) use the calculator to find the volume and surface area of the shed.
make sure to include the correct units.
volume:
surface area:
(b) the shed is painted yellow.
which measure helped the shed maker know how much paint to buy?
○ volume ○ surface area
(c) the shed is used for storage.
which measure would be used to find how much the shed holds?
○ volume ○ surface area

Explanation:

Part (a)

To find the volume and surface area of a rectangular prism (the shed), we use the following formulas:

• Volume of a rectangular prism: \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height.
• Surface area of a rectangular prism (including the floor): \( SA = 2(lw + lh + wh) \), since the shed has a floor (so we include all six faces).

Given:

• Length (\( l \)) = 12 ft
• Width (\( w \)) = 9 ft
• Height (\( h \)) = 10 ft

Step 1: Calculate the Volume

Using the volume formula:
\( V = l \times w \times h \)
Substitute the values:
\( V = 12 \times 9 \times 10 \)
\( V = 1080 \) cubic feet (\( ft^3 \))

Step 2: Calculate the Surface Area

Using the surface area formula:
\( SA = 2(lw + lh + wh) \)
Substitute the values:
\( SA = 2((12 \times 9) + (12 \times 10) + (9 \times 10)) \)
First, calculate each term inside the parentheses:

• \( 12 \times 9 = 108 \)
• \( 12 \times 10 = 120 \)
• \( 9 \times 10 = 90 \)

Now, sum these terms:
\( 108 + 120 + 90 = 318 \)

Then multiply by 2:
\( SA = 2 \times 318 = 636 \) square feet (\( ft^2 \))

Part (b)

To determine how much paint to buy, we need to know the area to be painted. Paint covers a surface, so the surface area of the shed (the total area of the exterior faces) is the relevant measure. Volume measures the space inside, which is not related to the amount of paint needed.

Part (c)

To find how much the shed holds (i.e., the capacity for storage), we need to know the volume of the shed. Volume measures the amount of space inside a three - dimensional object, while surface area measures the area of the outer surfaces. So volume is the relevant measure here.

Answer:

s:
(a)

• Volume: \( 1080\ ft^3 \)
• Surface area: \( 636\ ft^2 \)

(b) Surface area

(c) Volume