Question

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Question
Use the image to answer the question.

An illustration shows a rectangular prism. The top, front, and right faces are visible. The edges that are not visible are indicated by a dashed line. The base is labeled upper B equals 240 centimeters squared. The bottom front edge is labeled l equals 24 centimeters. A vertical edge is labeled h equals 8 centimeters.

Find the volume of the right rectangular prism.

(1 point)
cm3

Answer 1

[AI-generated answer — Bot GPT 3.5]

The formula to find the volume of a rectangular prism is V = l x w x h, where l is the length, w is the width, and h is the height.

From the image:
- The length (l) is given as 24 centimeters.
- The base (area of the top face) is given as 240 square centimeters, which can be expressed as length x width. Since the width is not given, we can calculate it by dividing the base by the length: 240 cm^2 / 24 cm = 10 cm. So, the width (w) is 10 centimeters.
- The height (h) is given as 8 centimeters.

Now, we can calculate the volume:
V = 24 cm x 10 cm x 8 cm
V = 1920 cm^3

Therefore, the volume of the right rectangular prism is 1920 cubic centimeters.

Answer 2

Using the formula V=B×h , what is the volume of a rectangular prism with a length of 714 m, a width of 1012 m, and a height of 1225 m? Your answer should be a mixed number in simplest form.(1 point)

m3

Answer 3

[AI-generated answer — Bot GPT 3.5]

Given values:

Length (l) = 714 m
Width (w) = 1012 m
Height (h) = 1225 m

Using the formula V = B x h, where B is the area of the base and h is the height, we first need to calculate the area of the base:
B = l x w
B = 714 m x 1012 m
B = 722568 m^2

Now, we can calculate the volume:
V = B x h
V = 722568 m^2 x 1225 m
V = 885582600 m^3

Therefore, the volume of the rectangular prism is 885,582,600 cubic meters.

Answer 4

Using the formula V=B×h , what is the volume of a rectangular prism with a length of 7/1/4 m, a width of 10/1/2 m, and a height of 12/2/5 m? Your answer should be a mixed number in simplest form.(1 point)

m3

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the volume of the rectangular prism with given dimensions, we will use the formula V = B x h, where B is the area of the base and h is the height.

Given dimensions:
Length (l) = 7 1/4 meters
Width (w) = 10 1/2 meters
Height (h) = 12 2/5 meters

First, we need to convert the mixed numbers to improper fractions for calculation:
7 1/4 = 29/4 meters
10 1/2 = 21/2 meters
12 2/5 = 62/5 meters

Now, calculate the area of the base:
B = l x w
B = (29/4) x (21/2)
B = (29 x 21) / (4 x 2)
B = 609 / 8 square meters

Now, calculate the volume:
V = B x h
V = (609/8) x (62/5)
V = (609 x 62) / (8 x 5)
V = 37818 / 40 cubic meters
V = 945.45 cubic meters

Therefore, the volume of the rectangular prism is 945.45 cubic meters.

Answer 6

n aquarium has a volume of 432 in.3 and a base of 96 in.2 . How would you write an equation to model finding the height of the aquarium?(1 point)

Responses

h=96(432)
h equals 96 left parenthesis 432 right parenthesis

h=96432
h equals Start Fraction 96 over 432 End Fraction

96=432h
96 equals 432 h

432=96h
pick the right answer

Answer 7

[AI-generated answer — Bot GPT 3.5]

The correct equation to model finding the height of the aquarium would be:

432 = 96h

Answer 8

A storage bin must be 6 inches high to fit between two shelves but must contain at least 178 in.3 . How would you write an inequality to express the possible area, b , of the base of the bin?(1 point)

b

Answer 9

[AI-generated answer — Bot GPT 3.5]

To express the possible area, b, of the base of the bin in terms of an inequality, we need to consider that the volume of a rectangular prism (storage bin) is given by the formula V = b x h, where b is the area of the base and h is the height.

Given that the height h must be at least 6 inches and the volume V must be at least 178 in^3, we can write the inequality as:
b x 6 ≥ 178

This inequality states that the base area multiplied by the height (at least 6 inches) must be greater than or equal to 178 cubic inches to meet the minimum volume requirement.