Question

the figure below shows a shed in the shape of a rectangular prism. note that the shed has a floor.
(a) use the calculator to find the surface area and volume of the shed. make sure to include the correct units.
surface area:
volume:
(b) the shed is used for storage. which measure would be used to find how much the shed holds?
○ surface area ○ volume
(c) the shed is made of metal. which measure helped the shed maker know how much metal was needed?
○ surface area ○ volume

Explanation:

Part (a)

Surface Area Calculation

The formula for the surface area \( SA \) of a rectangular prism is \( SA = 2(lw + lh + wh) \), where \( l = 6 \) ft, \( w = 3 \) ft, and \( h = 9 \) ft.

Step 1: Calculate each term

• \( lw = 6 \times 3 = 18 \) square feet
• \( lh = 6 \times 9 = 54 \) square feet
• \( wh = 3 \times 9 = 27 \) square feet

Step 2: Substitute into the formula

\( SA = 2(18 + 54 + 27) \)
\( SA = 2(99) \)
\( SA = 198 \) square feet

Volume Calculation

The formula for the volume \( V \) of a rectangular prism is \( V = lwh \).

Step 1: Substitute the values

\( V = 6 \times 3 \times 9 \)

Step 2: Calculate the product

\( V = 162 \) cubic feet

Part (b)

To find how much the shed holds (i.e., the amount of space inside), we use the volume. Surface area measures the total area of the outer surfaces, while volume measures the space enclosed. So the correct measure is Volume.

Part (c)

To determine how much metal is needed to make the shed, we need to know the total area of the metal sheets used, which is the surface area. Volume measures the space inside, not the material needed for the structure. So the correct measure is Surface area.

Final Answers

(a)

Surface area: \( \boldsymbol{198} \) square feet
Volume: \( \boldsymbol{162} \) cubic feet

(b)

\( \boldsymbol{\text{Volume}} \)

(c)

\( \boldsymbol{\text{Surface area}} \)

Answer:

Part (a)

Surface Area Calculation

The formula for the surface area \( SA \) of a rectangular prism is \( SA = 2(lw + lh + wh) \), where \( l = 6 \) ft, \( w = 3 \) ft, and \( h = 9 \) ft.

Step 1: Calculate each term

• \( lw = 6 \times 3 = 18 \) square feet
• \( lh = 6 \times 9 = 54 \) square feet
• \( wh = 3 \times 9 = 27 \) square feet

Step 2: Substitute into the formula

\( SA = 2(18 + 54 + 27) \)
\( SA = 2(99) \)
\( SA = 198 \) square feet

Volume Calculation

The formula for the volume \( V \) of a rectangular prism is \( V = lwh \).

Step 1: Substitute the values

\( V = 6 \times 3 \times 9 \)

Step 2: Calculate the product

\( V = 162 \) cubic feet

Part (b)

To find how much the shed holds (i.e., the amount of space inside), we use the volume. Surface area measures the total area of the outer surfaces, while volume measures the space enclosed. So the correct measure is Volume.

Part (c)

To determine how much metal is needed to make the shed, we need to know the total area of the metal sheets used, which is the surface area. Volume measures the space inside, not the material needed for the structure. So the correct measure is Surface area.

Final Answers

(a)

Surface area: \( \boldsymbol{198} \) square feet
Volume: \( \boldsymbol{162} \) cubic feet

(b)

\( \boldsymbol{\text{Volume}} \)

(c)

\( \boldsymbol{\text{Surface area}} \)