a solid cylinder has total surface are of 462 cm2 and its lateral surface area is one-third of its total - Maths - Surface Areas and Volumes

Question

a solid cylinder has total surface are of 462 cm2 and
its lateral surface area is one-third of its total surface area
find the volume of the cylinder

Ishan Goyal · Accepted Answer

Let the radius and height of the cylinder be r cm and h cm respectively.

Given, Total surface area of the cylinder = 462 cm²

∴ 2π r (r + h) = 462 cm² ...(1)

Lateral surface area of cylinder $rn rn = rn \frac{rn}{rn 1 rn} rn rn$ × Total surface area of cylinder (Given)

∴ 2π rh $rn rn = rn \frac{rn}{rn 1 rn} rn rn$ × 462 = 154 cm² ...(2)

From (1) and (2), we have

$rn rn \frac{rn}{rn 2 rn π rn rn rn r rn rn rn rn rn (rn r rn rn rn rn + rn rn rn rn rn h rn) rn rn} rn = rn \frac{rn}{rn 462 rn} rn rn ∴ rn \frac{rn}{rn r rn rn rn rn + rn rn rn h rn} rn = rn 3 rn rn \Rightarrow rn 3 rn h rn = rn r rn + rn h rn rn \Rightarrow rn r rn = rn 2 rn h rn rn$

From (2), we have

$rn rn π rn r rn rn rn rn rn rn �/mi>rnrnrnrnrnrnrrn=rn154rnrnrn{rn}^{rn cm rn rn rn 2 rn rn}rnrnrnrnrnrnrnrnrnrnrnrnrnrnrnrnrnrnrnrnrnrnrnrnrn[rn∵rnrrn=rn2rnhrn]rnrn∴rn\frac{rn}{rn 22 rn}rn{rn}^{rn r rn rn rn 2 rn rn}rn=rn154rnrnrn{rn}^{rn cm rn rn rn 2 rn rn}rnrn\Rightarrowrn{rn}^{rn r rn rn rn 2 rn rn}rn=rn\frac{rn}{rn 154 rn rn rn rn rn rn �/mi>rnrnrnrnrnrnrn7rn}rn{rn}^{rn cm rn rn rn 2 rn rn}rn=rn49rn{rn}^{rn cm rn rn rn 2 rn rn}rnrn\Rightarrowrnrrn=rn7rnrncmrn rn$

When r = 7 cm, we get

$rn rn h rn = rn \frac{rn}{rn r rn} rn = rn \frac{rn}{rn 7 rn} rn cm rn rn$

∴ Volume of the cylinder $rn rn = rn π rn {rn}^{rn r rn rn rn 2 rn rn} rn h rn = rn \frac{rn}{rn 22 rn} rn rn rn rn rn rn �/mi>rnrnrnrnrnrnrn{rn}^{rn (rn 7 rn cm rn) rn rn rn 2 rn rn}rnrnrnrnrnrn�/mi>rnrnrnrnrnrnrn\frac{rn}{rn 7 rn}rn{rn}^{rn cm = 539 �cm rn rn rn 3 rn rn}rn rn$

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a solid cylinder has total surface are of 462 cm2 and its lateral surface area is one-third of its total surface area . find the volume of the cylinder.

a solid cylinder has total surface are of 462 cm² and its lateral surface area is one-third of its total surface area . find the volume of the cylinder.