Question

the ratio between the curved surface area and total surface area of a right circular cylinder is 1:2. find the volume of the cylinder if it's total surface area is 616cm²

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Answer 1

Answer:

Given that:Curved surface area : Total surface area =1:2

Curved surface area :616=1:2

Curved surface area=

2

616

=308

⇒

2πr(h+r)

2πrh

=

2

1

⇒

h+r

h

=

2

1

⇒2h=h+r

⇒h=r

Curved Surface area=2πrh=2πr

2

=308 since h=r

⇒2×

7

22

r

2

=308

⇒r

2

=

44

308×7

=49

⇒r=7cm

Since r=h

h=7cm

Volume of the cylinder=πr

2

h=

7

22

×7×7×7=1078cm

3

∴ Volume of the cylinder is 1078 cu cm.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given that:Curved surface area : Total surface area =1:2

Curved surface area :616=1:2

Curved surface area=2616=308

⇒2πr(h+r)2πrh=21

⇒h+rh=21

⇒2h=h+r

⇒h=r

Curved Surface area=2πrh=2πr2=308 since h=r

⇒2×722r2=308

⇒r2=44308×7=49

⇒r=7cm

Since r=h

h=7cm

Volume of the cylinder=πr2h=722×7×7×7=1078cm3

∴ Volume of the cylinder is 1078 cu cm.