The picture shows two sizes of shipping boxes with measurements in inches. The boxes are rectangular prisms.
There are two rectangular prisms. Prism 1 has a height of 10 inches, length of 20 inches and a width of 7 inches. Prism 2 is smaller and to the right of Prism 1. Prism 2 has a height of 4 inches, length is 20 inches and width is 4 inches.
Marcus shipped 1 of the larger boxes and 2 of the smaller boxes. Which equations show the total volume of the boxes Marcus shipped? Select the three equations that apply.
A.
(
20
×
10
×
7
)
+
[
2
×
(
20
×
4
×
4
)
]
B.
(
20
×
10
×
7
)
×
[
2
×
(
20
×
4
×
4
)
]
C.
(
20
×
10
×
7
)
+
(
20
×
4
×
4
)
+
(
20
×
4
×
4
)
D.
(
20
+
10
+
7
)
+
(
20
+
4
+
4
)
+
(
20
+
4
+
4
)
E.
(
20
×
10
×
7
)
+
[
2
+
(
20
×
4
×
4
)
]
F.
(
200
×
7
)
+
[
2
×
(
80
×
4
)
]
To find the total volume of the boxes Marcus shipped, we need to calculate the volumes of each individual box and then add them together. The volume of a rectangular prism is found by multiplying its length, width, and height.
For Prism 1:
Volume of Prism 1 = length × width × height = 20 × 7 × 10
For Prism 2:
Volume of Prism 2 = length × width × height = 20 × 4 × 4
To get the total volume, we need to add the volumes of Prism 1 and twice the volume of Prism 2 (since Marcus shipped 2 of the smaller boxes).
So the equations that show the total volume of the boxes Marcus shipped are:
A. (20 × 10 × 7) + [2 × (20 × 4 × 4)]
- This equation correctly calculates the total volume. It adds the volume of Prism 1 and twice the volume of Prism 2.
C. (20 × 10 × 7) + (20 × 4 × 4) + (20 × 4 × 4)
- This equation also correctly calculates the total volume. It adds the volume of Prism 1, Prism 2 (once), and Prism 2 (once) again.
E. (20 × 10 × 7) + [2 + (20 × 4 × 4)]
- This equation is similar to equation A, but it incorrectly adds the number 2 to the volume of Prism 2. It should multiply the volume of Prism 2 by 2 instead of adding it.
Therefore, the correct equations are A, C, and E.