A solid cylinder has total surface area of 462 cm2 . If total surface area of the cylinder is thrice of its
curved surface are(a) then the volume of the cylinder is:
(a) 539 cm3
(b) 545 cm3
(c) 531 cm3
(d) 562 cm3
Answers
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Answer:
Given, total surface area of cylinder = 462 square cm.
Also, CSA of cylinder =
3
TSA of cylinder
⇒TSA=2πrh+2πr
2
⇒TSA=CSA+2πr
2
⇒TSA=
3
TSA
+2πr
2
⇒
3
2TSA
=2πr
2
⇒
3
TSA
=πr
2
⇒
3
462
=
7
22
×r
2
⇒r=7cm
Now, CSA of cylinder =
3
TSA of cylinder
=
3
462
=154cm
2
⇒2πrh=154
⇒2×
7
22
×7×h=154
⇒h=
2
7
cm
Therefore, volume of the cylinder =πr
2
h
=
7
22
×7
2
×
2
7
=539cm
3
Hence, volume of the solid cylinder is 539cm
3
.
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