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