SSC CPO SI and ASI 2016 Paper

Question : 147 of 200

Marks: +1, -0

The curved surface area of a cylinder, with its height equal to its radius, is equal to the curved surface area of a sphere. The ratio of volume of the cylinder to that of the sphere is

$√2 : 3$
$3 : √2$
$2√2 : 3$
$3 : 2√2$

Validate

Solution:

(2) Let radii of cylinder and sphere be r

_{c}

and r

_{s}

, respectively. Since, curved surface areas are equal,

2 \π r_{c}^{2}=4 \πr_{s}^{2} ⇒ r_{c}=r_{s}√{2}

Now, ratio of volume of cylinder to that of sphere is

{\π r_{c}^{3}}/{ {4}/{3} \π r_{s}^{3}}

= {3× 2 √{2}}/{4}= {3}/{√{2}}=3 : √{2}

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