a rectangular pyramid has a length of 7cm and width of 9cm. its volume is 231 cubic cm. 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 cubic cm
Substitute the values into the formula:
231 = (1/3) * 7 * 9 * h
231 = (63/3) * h
231 = 21h
h = 231 / 21
h = 11
Therefore, the height of the rectangular pyramid is 11 cm.
alight now show an invorrect way to solve this
Sure! Here is an incorrect way to solve this problem:
Given:
- Length = 7 cm
- Width = 9 cm
- Volume = 231 cubic cm
Incorrect calculation:
V = (1/3) * length * width * height
231 = (1/3) * 7 * 9 * h
231 = 21h
h = 231 / 21
h = 11
This calculation does not take into account that the height is actually perpendicular to the base, which means it should be the height of the pyramid, not only calculated from the three lengths. So, this incorrect method led to the correct answer, but it was due to coincidence rather than correct reasoning.