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An illustration shows a rectangular pyramid with a length of 10 decimeters, a width of 4 decimeters, a perpendicular height of 10 decimeters, and a slant height of 11.18 decimeters. The right and front faces are visible. Edges and faces that are not visible are indicated by dashed lines.
What is the volume of the pyramid? Round to the nearest hundredth.
(1 point)
Responses
400 dm3
400 dm cubed
447.2 dm3
447.2 dm cubed
133.33 dm3
133.33 dm cubed
149.07 dm3
149.07 dm cubed
To find the volume of a pyramid, you can use the formula:
Volume = (1/3) * base area * height
The base of the pyramid is a rectangle with dimensions 10 dm by 4 dm, so the base area is:
Base area = 10 dm * 4 dm = 40 dm^2
Now, plug in the base area of 40 dm^2 and the height of 10 dm into the volume formula:
Volume = (1/3) * 40 dm^2 * 10 dm = 133.33 dm^3
Therefore, the volume of the pyramid is 133.33 dm^3. The closest answer choice is:
133.33 dm3
To find the volume of a rectangular pyramid, you can use the formula:
Volume = (1/3) * base area * height
The base of the watermelon slice is a rectangle with dimensions 1 in by 10.5 in, so the base area is:
Base area = 1 in * 10.5 in = 10.5 in^2
Now, plug in the base area of 10.5 in^2 and the height of 8 in into the volume formula:
Volume = (1/3) * 10.5 in^2 * 8 in = 28 in^3
Therefore, the approximate volume of Nicol's watermelon slice is 28 in^3. The correct answer choice is:
28 in.3
The volume of a rectangular prism is given by the formula:
Volume = Base Area * Height
Since the base and height of the rectangular prism are congruent, let's denote the base area as B and the height as H.
For the rectangular prism, the volume is given as 600 in^3:
600 = B * H
Now, the volume of a rectangular pyramid is given by the formula:
Volume = (1/3) * Base Area * Height
Since the base area and height are congruent in this case, the volume of the rectangular pyramid would be:
Volume = (1/3) * B * H
Given that B * H = 600, the volume of the rectangular pyramid would be:
Volume = (1/3) * 600 = 200 in^3
Therefore, the volume of the rectangular pyramid whose base and height are congruent to the prism is 200 in^3. The correct answer choice is:
200 in.3
If a prism and a pyramid have congruent triangular bases and the same heights, then:
the volume of the pyramid is one-third the size of the volume of the prism.
This is because the volume of a prism is given by the formula: Volume = Base Area * Height
And the volume of a pyramid is given by the formula: Volume = (1/3) * Base Area * Height
Since the bases are congruent and the heights are the same, the base area and height of the pyramid is one-third the size of the base area and height of the prism. Therefore, the volume of the pyramid will be one-third of the volume of the prism.
Question
A slice of watermelon approximates the shape of a rectangular pyramid. Nicol’s slice is 1 inch wide, 1012
in. long, and 8 in. tall. What is the approximate volume of her watermelon slice? Round your answer to the nearest hundredth, if applicable.(1 point)
Responses
205 in.3
205 in. cubed
28 in.3
28 in. cubed
104.23 in.3
104.23 in. cubed
84 in.3
A rectangular pyramid has a base area of 16 in.2
, and a congruent rectangular prism has a volume of 288 in.3
. What is the height of the rectangular pyramid?(1 point)
Responses
18 in.
18 in.
96 in.
96 in.
54 in.
54 in.
6 in.
The volume of a rectangular prism is given by the formula:
Volume = Base Area * Height
Since the volume of the congruent rectangular prism is 288 in^3 and the base area of the rectangular pyramid is 16 in^2, we can set up the following equation:
16 in^2 * Height = 288 in^3
Solving for Height:
Height = 288 in^3 / 16 in^2 = 18 in
Therefore, the height of the rectangular pyramid is 18 inches. The correct answer choice is:
18 in.
If the volume of a rectangular prism is 600 in.3
, what is the volume of a rectangular pyramid whose base and height is congruent to the prism?(1 point)
Responses
1,200 in.3
1,200 in. cubed
200 in.3
200 in. cubed
300 in.3
300 in. cubed
1,800 in.3
If a prism and a pyramid have congruent triangular bases and the same heights, then(1 point)
Responses
the volume of the pyramid and the volume of the prism are the same.
the volume of the pyramid and the volume of the prism are the same.
the volume of the prism is 13
the size of the volume of the pyramid.
the volume of the prism is Start Fraction 1 over 3 End Fraction the size of the volume of the pyramid.
the volume of the pyramid is three times as large as the volume of the prism.
the volume of the pyramid is three times as large as the volume of the prism.
the volume of the pyramid is 13
the size of the volume of the prism.
the volume of the pyramid is Start Fraction 1 over 3 End Fraction the size of the volume of the prism.
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An illustration shows a triangle with sides measuring 14, 12, and 6. A perpendicular line, from the side measuring 14 to the opposite angle, measures 5. A right angle symbol is shown to the left of the perpendicular line.
A prism and a pyramid both have this triangular base. If both shapes have the same height and the volume of the pyramid is 210 cubic units, what is the volume of the prism?
(1 point)
Responses
210 cubic units
210 cubic units
1,260 cubic units
1,260 cubic units
70 cubic units
70 cubic units
630 cubic units