Question

Question number 17. ​

Answer 1

Answer:

  1078$m^{3}$

Step-by-step explanation:

given , tsa of cylinder = 616$m^{2}$
ATQ-
csa of cylinder / tsa of cylinder = 1/2
⇒2$\pi$rh/2$\pi$r(h+r) = 1/2
⇒h/h+r = 1/2
⇒2h = h+r
⇒r=h                                                     .....(i)
tsa of cylinder= 2$\pi$r(h+r)
⇒616 = 2×22×h(h+h)/7                  (from eqn. i)
⇒98 = h(2h)
⇒98 = 2 $h^{2}$
⇒$h^{2}$ = 49
⇒h=7 0r -7          
negative value be rejected.

so , h=r=7
volume of cylinder = $\pi r^{2} h$
⇒2×22×7×7×7/7
⇒1078$m^{3$

Answer 2

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Class 9

>>Maths

>>Surface Areas and Volumes

>>Volume of Cube, Cuboid and Cylinder

>>The ratio between the curved surface are

Question

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The ratio between the curved surface area and the total surface area of a right circular cylinder is 1:2. Find the volume of the cylinder if its total surface area is 616 cm sq.

Medium

Solution

verified

Verified by Toppr

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