Question

What is the volume of a cube with a side length of 1.5 in.?(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The volume of a cube is calculated by taking the length of one side and cubing it.

Volume = side length^3

Volume = (1.5)^3
Volume = 3.375 cubic inches

Therefore, the volume of a cube with a side length of 1.5 in. is 3.375 cubic inches.

Answer 2

If the volume of a right rectangular prism is 1.5 in.3 and its length and width have a product of 1.5 in.2 , what is the height of this prism? (1 point)

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the height of the prism, we can set up an equation using the volume and the product of the length and width.

Let:
- Length = L
- Width = W
- Height = H
- Volume = 1.5 in^3
- Product of length and width = 1.5 in^2

Volume = Length x Width x Height
1.5 = 1.5 x 1.5 x H
1.5 = 2.25H
H = 1.5 / 2.25
H = 0.67

Therefore, the height of the right rectangular prism is 0.67 inches.

Answer 4

Lloyd bought a refrigerator that measures 76 cm×76 cm×170 cm to fit in a space with a volume of 975,000 cm3 . Will the refrigerator fit in the space? Explain.(1 point)

Answer 5

[AI-generated answer — Bot GPT 3.5]

To determine if the refrigerator will fit in the space with a volume of 975,000 cm^3, we need to calculate the volume of the refrigerator and compare it to the space available.

Given dimensions of the refrigerator:
Length = 76 cm
Width = 76 cm
Height = 170 cm

Volume of the refrigerator:
Volume = Length x Width x Height
Volume = 76 cm x 76 cm x 170 cm
Volume = 975,200 cm^3

Since the volume of the refrigerator is 975,200 cm^3, it is larger than the space available, which is 975,000 cm^3. Therefore, the refrigerator will not fit in the space as it is slightly larger than the available space.

Answer 6

A slice of cheese is cut from a wheel of parmesan, and the wedge approximates the shape of a rectangular pyramid. Its base is 4 cm wide and 9 cm long. The wedge is 21 cm tall. What is the volume of the piece of cheese?(1 point)

Answer 7

[AI-generated answer — Bot GPT 3.5]

The volume of a rectangular pyramid can be calculated using the formula:

Volume = (1/3) x base area x height

Given:
Base width = 4 cm
Base length = 9 cm
Height = 21 cm

First, calculate the area of the base:
Base area = base width x base length
Base area = 4 cm x 9 cm
Base area = 36 cm^2

Now, calculate the volume of the pyramid using the formula:

Volume = (1/3) x base area x height
Volume = (1/3) x 36 cm^2 x 21 cm
Volume = 252 cm^3

Therefore, the volume of the piece of cheese is 252 cubic centimeters.

Answer 8

A rectangular prism has a volume of 27 in.3 . If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?(1 point)

Answer 9

[AI-generated answer — Bot GPT 3.5]

The volume of a rectangular prism is equal to the volume of a rectangular pyramid with the same base and height.

Given:
Volume of the rectangular prism = 27 in^3

Since the pyramid has the same base and height as the prism, the volume of the pyramid will be equal to 1/3 of the volume of the prism, using the formula for the volume of a pyramid:

Volume of the pyramid = (1/3) x volume of the prism
Volume of the pyramid = (1/3) x 27 in^3
Volume of the pyramid = 9 in^3

Therefore, the volume of the pyramid is 9 cubic inches.