Two square pyramids have the same volume. For the first pyramid, the side length of the base is 20 in., and the height is 21 in. The second pyramid has a height of 84 in. What is the side length of the base of the second pyramid?
Solution:
The volume of a square pyramid = 1/3a2h
Where a is the base length
h is the height
Side length of base = 20 inches
Height = 21 inches
Substituting it in the formula, we get
Volume of first pyramid = 1/3 × 202 × 21
By further calculation
= 1/3 × 400 × 21
= 2800 inches3
As volume of both the equations is same
V = 2800 inches3
a = ?
h = 84 inches
Substituting it in the formula
2800 = 1/3 × a2 × 84
So we get
a2 = [2800 × 3]/ 84
a2 = 100
a = 10 inches
Therefore, the side length of the base of the second pyramid is 10 inches.
Two square pyramids have the same volume. For the first pyramid, the side length of the base is 20 in., and the height is 21 in. The second pyramid has a height of 84 in. What is the side length of the base of the second pyramid?
Summary:
Two square pyramids have the same volume. For the first pyramid, the side length of the base is 20 in., and the height is 21 in. The second pyramid has a height of 84 in. The side length of the base of the second pyramid is 10 inches.