To find the height of the rectangular prism, we need to first find the dimensions of the congruent base of the pyramid since the base of the prism is also the same.
The volume of a pyramid is given by the formula:
Volume = (1/3) * base area * height
Given that the volume of the pyramid is 20 cm3 and the base area is 15 cm2:
20 = (1/3) * 15 * height
20 = 5 * height
height = 4 cm
Now, the height of the rectangular prism will also be 4 cm.
Therefore, the correct answer is:
4 cm
A rectangular prism has a base area of 15 cm2 , and pyramid with a congruent base and height has a volume of 20 cm3 . What is the height of the rectangular prism?(1 point) Responses 20 cm 20 cm 4/3 cm Start Fraction 4 over 3 End Fraction cm 4 cm 4 cm 5 cm 5 cm
5 answers
Use the model for the base of a triangular prism and triangular pyramid. If the heights are both 9 cm, what is the volume of each shape? (1 point) Responses prism: 72 cm3; pyramid: 216 cm3 prism: 72 cm cubed ; pyramid: 216 cm cubed prism: 216 cm3; pyramid: 72 cm3 prism: 216 cm cubed ; pyramid: 72 cm cubed prism: 108 cm3; pyramid: 36 cm3 prism: 108 cm cubed ; pyramid: 36 cm cubed prism: 36 cm3; pyramid: 108 cm3
For a prism, the volume is given by the formula:
Volume = base area * height
For a pyramid, the volume is given by the formula:
Volume = (1/3) * base area * height
Given that the heights of both shapes are 9 cm:
Base area of the prism = base area of the pyramid
If we let the base area be A, the volume of the prism will be A * 9 and the volume of the pyramid will be (1/3) * A * 9.
Since they both have the same base area, we can simplify the comparison by multiplying the volume of the pyramid by 3 to make the formulas match:
Volume of prism = A * 9
Volume of pyramid = A * 9
(1/3) * A * 9 * 3 = A * 9
So, the volume of the prism and the pyramid are equal.
Therefore, the correct answer is:
prism: 72 cm cubed; pyramid: 216 cm cubed
Volume = base area * height
For a pyramid, the volume is given by the formula:
Volume = (1/3) * base area * height
Given that the heights of both shapes are 9 cm:
Base area of the prism = base area of the pyramid
If we let the base area be A, the volume of the prism will be A * 9 and the volume of the pyramid will be (1/3) * A * 9.
Since they both have the same base area, we can simplify the comparison by multiplying the volume of the pyramid by 3 to make the formulas match:
Volume of prism = A * 9
Volume of pyramid = A * 9
(1/3) * A * 9 * 3 = A * 9
So, the volume of the prism and the pyramid are equal.
Therefore, the correct answer is:
prism: 72 cm cubed; pyramid: 216 cm cubed
How does the volume of the prism compare to the volume of the pyramid? (1 point) Responses The volume of the prism is 13 the size of the pyramid. The volume of the prism is Start Fraction 1 over 3 End Fraction the size of the pyramid. The volume of the prism is the same as the volume of the pyramid. The volume of the prism is the same as 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 prism is three times as large as the volume of the pyramid. The volume of the prism is three times as large as the volume of the pyramid.
The volume of the prism is equal to the volume of the pyramid. As shown in the previous calculation, both shapes have the same volume when the base area and heights are equal.
Therefore, the correct answer is:
The volume of the prism is the same as the volume of the pyramid.
Therefore, the correct answer is:
The volume of the prism is the same as the volume of the pyramid.