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Standard IX

Mathematics

Right Circular Cylinder

The volume of...

Question

The volume of a cylinder is $231 c m^{3}$ and its height is 6 $c m$ . A ball will fit inside the cylinder if its radius is ______.

3 $c m$

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4 $c m$

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2.5 $c m$

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5 $c m$

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Solution

The correct option is C
2.5 $c m$

Volume of cylinder $= π \times r^{2} \times h$
$\Rightarrow 231 = \frac{22}{7} \times r^{2} \times 6$
$\Rightarrow r^{2} = 231 \times \frac{7}{22} \times \frac{1}{6}$
$\Rightarrow r^{2} = 12.25$
$\Rightarrow r = 3.5$
So, a ball will fit inside the cylinder if its radius is less than or equal to 3.5 $c m$ .

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The volume of a cylinder is 231 cm3 and its height is 6 cm. A ball will fit inside the cylinder if its radius is ______.

The correct option is C 2.5 cm Volume of cylinder =π×r2×h ⇒231=227×r2×6 ⇒r2=231×722×16 ⇒r2=12.25 ⇒r=3.5 So, a ball will fit inside the cylinder if its radius is less than or equal to 3.5 cm.

The volume of a cylinder is $231 c m^{3}$ and its height is 6 $c m$ . A ball will fit inside the cylinder if its radius is ______.