Find the height of a pyramid with a volume of $960 in^3$ if the base is a square with a side length of 12 in.
Answer (1)
We are given the volume V and the side length s of the square base of the pyramid.
We use the formula for the volume of a pyramid with a square base: V = 3 1 s 2 h .
We substitute the given values into the formula and solve for h .
The height of the pyramid is 20 in .
Explanation
Problem Analysis We are given the volume of a pyramid, V = 960 i n 3 , and the side length of its square base, s = 12 in . We need to find the height, h , of the pyramid.
Volume Formula The formula for the volume of a pyramid with a square base is given by: V = 3 1 s 2 h
Substitution Substitute the given values into the formula: 960 = 3 1 ( 12 ) 2 h
Solving for h Now, we solve for h :
960 = 3 1 ( 144 ) h 960 = 48 h h = 48 960 h = 20
Final Answer Therefore, the height of the pyramid is 20 inches.
Examples
Understanding the volume of pyramids is useful in architecture and construction. For example, if you're designing a pyramid-shaped structure and need it to enclose a specific volume, you can use the volume formula to determine the necessary height given the dimensions of the base. This ensures the structure meets the required space needs while adhering to the desired aesthetic.
