The rectangular pyramid has a length of 7 cm and it width of 9 cm its volume is 231 cm³ 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:
Volume = (1/3) * base area * height
Given:
Length = 7 cm
Width = 9 cm
Volume = 231 cm³
Let's find the base area first. The base of the rectangular pyramid is a rectangle, so the base area is calculated as:
Base Area = Length * Width
Base Area = 7 cm * 9 cm
Base Area = 63 cm²
Now, we can substitute the known values into the formula and solve for the height:
231 cm³ = (1/3) * 63 cm² * height
Multiplying both sides of the equation by 3 to eliminate the fraction:
3 * 231 cm³ = 63 cm² * height
693 cm³ = 63 cm² * height
To isolate the height, divide both sides of the equation by 63 cm²:
693 cm³ / 63 cm² = height
11 cm = height
Therefore, the height of the rectangular pyramid is 11 cm.