Question:
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.
The formula for the volume of a rectangular pyramid is V = (1/3) * length * width * height.
Given:
Length = 7 cm
Width = 9 cm
Volume = 231 cm^3
We can substitute these values into the formula to find the height:
231 = (1/3) * 7 * 9 * height
Now we can solve for the height by multiplying both sides of the equation by 3 and dividing by (7 * 9):
231 * 3 = 7 * 9 * height
693 = 63 * height
Dividing both sides of the equation by 63:
693 / 63 = height
11 = height
Therefore, the height of the rectangular pyramid is 11 cm.
Sure! Here are the steps to calculate the height of the rectangular pyramid:
1. Given length = 7 cm, width = 9 cm, and volume = 231 cm^3.
2. Use the formula for the volume of a rectangular pyramid: V = (1/3) * length * width * height.
3. Substitute the given values into the formula: 231 = (1/3) * 7 * 9 * height.
4. Simplify the equation: 231 = 63 * height.
5. Divide both sides of the equation by 63: 231 / 63 = height.
6. Calculate the result: 11 = height.
7. Therefore, the height of the rectangular pyramid is 11 cm.