Question

10. The total surface area of a cylinder is 462 cm². Its curved surface area is one third of
its total surface area. Find radius and height of the cylinder.

Answer 1

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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