Question

A solid Cylinder has total surface
Gea of 462m². if its
Covered surface and is one
third of its total, oned find the
Volume of cylender​

Answer 1

Answer:

ANSWER

We have,

Curved surface area =

3

1

× Total surface area

⇒2πrh=

3

1

×(2πrh+2πr

2

)

⇒4πrh=2πr

2

⇒2h=r…(1)

Now, Total surface area=462

⇒ Curved surface area=

3

1

×462

⇒2πrh=154

⇒2×

7

22

×2h

2

=154

⇒h

2

=

2×22×2

154×7

=

4

49

⇒h=

2

7

cm.

From (1), r=7

Step-by-step explanation:

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Answer 2

Let r cm be the radius of the base and h cm be the height of the cylinder,

Then, total surface area of cylinder = 2πr (r + h)

Curved surface area of cylinder = 2πrh

We have,

Curved surface area = 1/3(Total surface area) = 1/3 x 462 cm2 = 154 cm2

⇒ 2πrh = 154

Also, 2πrh + 2πr2 = 462 ⇒ 154 + 2πr2 = 462

⇒ 2πr2 = 462 - 154 = 308 cm2

2 x 22/7 x r2 = 308

⇒ r2 = 308 x 7/2 x 22 = 72 ⇒ r = 7 cm

Again 2πrh = 154 ⇒ 2 x 22/7 x 7 x h = 154

⇒ h = 154/2 x 22 = 7/2 cm

Volume of the cylinder = πr2h

= 22/7 x 7 x 7 x 7/2 = 539 cm3

I guess this is the answer

Hope it helps