An oblique cylinder has a radius of 9 centimeters and a volume of 486 cubic centimeters. Use Cavalieri’s Principle to calculate the height of the solid.
5 meters
6 meters
7 meters
8 meters
Answers
8 meters of the cldr. must be
Using Cavalieri’s Principle the height of the solid is 6 cm.
Hi there,
I think there is a missing data in your question without which the answer will be completely different from the options given. Also, S.I. unit of the radius and volume is not the same in the question as in the option. I have rewritten the question and solved it using centimeter as the unit. Hope the answer is correct. Thanks
Q. An oblique cylinder has a radius of 9 centimeters and a volume of 486π cubic centimetres. Use Cavalieri’s Principle to calculate the height of the solid.
Step-by-step explanation:
The radius of the base of the oblique cylinder, r = 9 cm
The volume of the oblique cylinder, V = 486π cm³
- We know that Cavalieri’s Principle states that a group of parallel planes gives equal cross-sectional areas and the same height, then the volumes are equal.
- We find the volume of the oblique cylinder by multiplying the area of the base and the height, which is same as the volume of the regular cylinder.
∴ The Volume of the cylinder = πr²h
⇒ 486π = π(9)²h ...... [substituting the given values]
⇒ h = [486π] / [π * 81]
⇒ h = 6 cm
Thus, by using Cavalieri’s Principle, the height of the oblique cylinder comes out to be 6 cm.
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