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)
The volume of a pyramid is given by the formula:
Volume = (1/3) * base area * height
In this case, we know the volume is 231 cubic centimeters, and the base has a length of 7 cm and a width of 9 cm. Let's calculate the base area first:
Base area = length * width
= 7 cm * 9 cm
= 63 square cm
Now we can plug in the known values into the volume formula and solve for the height:
231 cm³ = (1/3) * 63 cm² * height
To isolate the height, we can multiply both sides of the equation by 3:
3 * 231 cm³ = 63 cm² * height
693 cm³ = 63 cm² * height
Now let's divide both sides of the equation by 63 cm² to solve for the height:
693 cm³ / 63 cm² = height
11 cm = height
Therefore, the height of the pyramid is 11 cm.