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 and please show all your work.(2 points)
The formula for the volume of a rectangular pyramid is given by:
Volume = (1/3) x Base Area x Height
In this case, we are given the length and width of the rectangular base, and the volume. We can use these values to find the height.
Given:
Length of rectangular base = 7 cm
Width of rectangular base = 9 cm
Volume of pyramid = 231 cm^3
Let's calculate the base area first:
Base Area = Length x Width
Base Area = 7 cm x 9 cm
Base Area = 63 cm^2
Now, let's plug in the values in the volume formula:
231 cm^3 = (1/3) x (63 cm^2) x Height
To find the height, we can rearrange the equation:
Height = (3 x 231 cm^3) / (63 cm^2)
Height = 3.6667 cm (rounded to four decimal places)
Therefore, the height of the pyramid is approximately 3.6667 cm.