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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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