Question

te that the box has a lid.
(a) use the calculator to find the surface area and volume of the box.
make sure to include the correct units.
surface area:
volume:
(b) the box is to be filled with sand.
which measure would be used to find the amount of sand the box will hold?
○surface area ○volume
(c) the box was made from wood.
which measure helped the carpenter know how much wood to buy?
○surface area ○volume

Explanation:

Part (a)

Surface Area of the Box (Rectangular Prism with Lid)

A rectangular prism with a lid (a closed rectangular box) has a surface area formula of \( SA = 2(lw + lh + wh) \), where \( l \) is length, \( w \) is width, and \( h \) is height.

Given:

• Length (\( l \)) = 9 ft
• Width (\( w \)) = 4 ft
• Height (\( h \)) = 2 ft

Step 1: Calculate each pair of faces

First, calculate \( lw \), \( lh \), and \( wh \):

• \( lw = 9 \times 4 = 36 \) square feet
• \( lh = 9 \times 2 = 18 \) square feet
• \( wh = 4 \times 2 = 8 \) square feet

Step 2: Apply the surface area formula

Now, substitute these values into the formula:
\( SA = 2(36 + 18 + 8) \)
First, add the values inside the parentheses: \( 36 + 18 + 8 = 62 \)
Then, multiply by 2: \( SA = 2 \times 62 = 124 \) square feet

Volume of the Box

The volume of a rectangular prism is given by the formula \( V = l \times w \times h \).

Step 1: Substitute the values

Substitute \( l = 9 \), \( w = 4 \), and \( h = 2 \) into the formula:
\( V = 9 \times 4 \times 2 \)

Step 2: Calculate the volume

First, multiply 9 and 4: \( 9 \times 4 = 36 \)
Then, multiply by 2: \( 36 \times 2 = 72 \) cubic feet

Part (b)

To find the amount of sand the box will hold, we need to know the space inside the box. Volume measures the amount of space a three - dimensional object can hold. Surface area measures the total area of the outer surfaces. So, the measure used to find the amount of sand the box will hold is Volume.

Part (c)

The carpenter needs to know how much wood to buy to make the box. The wood is used to cover the surfaces of the box. Surface area measures the total area of all the faces of the box. Volume measures the space inside. So, the measure that helped the carpenter know how much wood to buy is Surface area.

Answer:

s:

Part (a)

• Surface area: \( \boldsymbol{124} \) square feet (\( \text{ft}^2 \))
• Volume: \( \boldsymbol{72} \) cubic feet (\( \text{ft}^3 \))

Part (b)

The measure used to find the amount of sand the box will hold is \(\boldsymbol{\text{Volume}}\) (select the "Volume" option).

Part (c)

The measure that helped the carpenter know how much wood to buy is \(\boldsymbol{\text{Surface area}}\) (select the "Surface area" option).