SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 62 of 100

Marks: +1, -0

A solid cylinder has the total surface area 231 square cm. If its curved surface area is

2 /3

of the total surface area, then the volume of the cylinder is

Solution:

(3) Let the radius of cylinder be r cm.
Height = h cm.
According to the question,

2 \π r h+2 \π r^{2}=231

Again,

2 \π r h= {2}/{3} × 231=154

∴ 2 \π r^{2}=231-154

⇒ 2 ×{22}/{7} r^{2}=77

⇒ r^{2}= {77× 7}/{22× 2}= {49}/{2 × 2}

∴ r= {7}/{2} {cm} .

∴ 2 \π r h=154

⇒ 2×{22}/{7} ×{7}/{2}× h=154

⇒22 h=154

⇒ h= {154}/{22}=7 {cm}

∴ Volume of cylinder

=πr^2h

= ( {22}/{7} ×{7}/{2}×{7}/{2} × 7 ) {cu} . {cm}

= 269.5 cu. cm.

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