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प्रश्न
The height of sand in a cylindrical shaped can drops 3 inches when 1 cubic foot of sand is poured out. What is the diameter, in inches, of the cylinder?
विकल्प
- \[\frac{24}{\pi}\]
- \[\frac{48}{\pi}\]
- \[\frac{32}{\pi}\]
- \[\frac{48}{\pi}\]
उत्तर
Let r be the radius of the cylinder. It is given that the height drops 3 inches, when 1 cubic foot of sand is poured out and 1 foot = 12 inch
So,
`12xx12xx12 = pi r^2 h`
`⇒ 12 xx 12 xx 12 = pi r^2 xx 3`
`⇒ r^2 = (12 xx 12 xx 4)/pi`
`⇒ r = 24/sqrt(pi)`
`⇒ 2r = 48/sqrt(pi)`
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