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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? - Mathematics

MCQ

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?

Options

  • \[\frac{24}{\pi}\]

     

  • \[\frac{48}{\pi}\]

     

  • \[\frac{32}{\pi}\]

     

  • \[\frac{48}{\pi}\]

     

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Solution

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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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 19 Surface Areas and Volume of a Circular Cylinder
Q 18 | Page 30
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