A rectangular pyramid has a length of 7 cm and a width of 9 cm. Its volume is 231 cubic centimeters. Use the formula for the volume of a pyramid to calculate the height of this pyramid. Show all your work.(2 points)
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Sure! To find the height of a rectangular pyramid, we can use the formula for the volume of a pyramid, which is given by:
Volume = (1/3) * base area * height
Given that the length of the rectangular pyramid is 7 cm and the width is 9 cm, we can find the base area by multiplying the length and width:
Base area = length * width
Base area = 7 cm * 9 cm
Base area = 63 square cm
Now, we can rearrange the formula for the volume of a pyramid to solve for the height:
Volume = (1/3) * base area * height
231 cubic cm = (1/3) * 63 square cm * height
To find the height, we can isolate it:
231 cubic cm = (1/3) * 63 square cm * height
height = (231 cubic cm * 3) / (63 square cm)
height = 693 cubic cm / 63 square cm
height = 11 cm
Therefore, the height of the rectangular pyramid is 11 cm.
make it a text
Sure! To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid: Volume = (1/3) * base area * height
Given that the length of the pyramid is 7 cm and the width is 9 cm, we can find the base area by multiplying the length and width: Base area = 7 cm * 9 cm = 63 square cm
Now, we can rearrange the formula to solve for the height: Volume = (1/3) * base area * height --> height = (Volume * 3) / base area
Substituting the given volume of 231 cubic cm and the calculated base area of 63 square cm, we have: height = (231 cubic cm * 3) / 63 square cm = 693 cubic cm / 63 square cm = 11 cm
Therefore, the height of the rectangular pyramid is 11 cm.