A frustum of a pyramid is 16cm square at the bottom 6cm squat at the top and 12cm high, find the volume of the frustum
Find the volume if it had a pointy top
(1/3) * area of base * height including top that got removed
Find the volume of the top that got removed
Subtract
A frustum of a pyramid is 16cm square at the bottom. 6cm square at the top, and 12cm high. Find the volume of the frustum
To find the volume of a frustum of a pyramid, you can use the formula:
V = (1/3) * h * (A1 + A2 + √(A1 * A2))
Where:
V is the volume of the frustum,
h is the height of the frustum,
A1 is the area of the lower base, and
A2 is the area of the upper base.
In this case, the dimensions you have provided are:
Bottom base side length (b1) = 16 cm
Top base side length (b2) = 6 cm
Height (h) = 12 cm
First, let's calculate the areas of the bases:
A1 = b1^2 = 16^2 = 256 cm^2
A2 = b2^2 = 6^2 = 36 cm^2
Now, substitute the values into the formula:
V = (1/3) * 12 * (256 + 36 + √(256 * 36))
V = (1/3) * 12 * (292 + √(9216))
V = (1/3) * 12 * (292 + 96)
V = (1/3) * 12 * 388
V = 1552 cm^3
Therefore, the volume of the frustum is 1552 cubic centimeters.