1
Question
In two square pyramids of the same volume, the base edge of one is half the base edge of the other. How many times the height of the pyramid with larger base is the height of the other?
In two square pyramids of the same volume, the base edge of one is half the base edge of the other. How many times the height of the pyramid with larger base is the height of the other?
Open in App
Solution
Let the base edge of the second pyramid be b units.
∴ Base edge of the first pyramid = 
units
Let the height of the first and the second pyramid be h1 units and h2 units respectively.
Base area of the first pyramid = ( units)2 = 
sq. units
Base area of the second pyramid = (b units)2 = b2 sq. units
Volume of square pyramid = 
Base area × Height
According to given condition:
Volume of the first pyramid = Volume of the second pyramid
Therefore, the height of the pyramid with larger base is one-fourth times the height of the other.
Let the base edge of the second pyramid be b units.
∴ Base edge of the first pyramid = units
Let the height of the first and the second pyramid be h1 units and h2 units respectively.
Base area of the first pyramid = ( units)2 = sq. units
Base area of the second pyramid = (b units)2 = b2 sq. units
Volume of square pyramid = Base area × Height
According to given condition:
Volume of the first pyramid = Volume of the second pyramid
Therefore, the height of the pyramid with larger base is one-fourth times the height of the other.
Suggest Corrections
0
Similar questions