Question

A cylinder has a diameter of 20 cm . The area of the curved surface is 100 m square. Find the volume of the cylinder.​

Answer 1

Step-by-step explanation:

Diameter of cylinder = 20 cm

Radius (r) =

2

20

=10cm

CSA=1000cm

3

2πrh=1000

2(3.14)(10)h=1000

h=

2(3.14)(10)

1000

=15.9cm

and volume = πr

2

2h

=(3.14)(10)

2

(15.9)

=4992.6cm

3

Answer 2

⠀⠀⠀⠀⠀⠀${\huge{\underbrace{\rm{Question}}}}$

A cylinder has a diameter of 20 cm . The area of the curved surface is 100 m square. Find the volume of the cylinder.

⠀⠀⠀⠀⠀⠀⠀${\huge{\underbrace{\rm{Answer}}}}$

⠀⠀

Given:

⠀⠀

Diameter of the cylinder is 20 cm

⠀⠀

Area of the curved surface is 100 m²

⠀

To find:

⠀⠀

Find the volume of the cylinder.

⠀⠀

Solution:

⠀⠀

Diameter of the cylinder = 20 cm

.°. Radius of the cylinder(r) = $\sf{\dfrac{20}{2}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\sf{\cancel{\dfrac{20}{2}}\:cm}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 10 cm

⠀⠀

the curved surface area of the cylinder = 100 m²

Let, the height of the cylinder is h cm

⠀⠀

We know that,

⠀⠀⠀$\boxed{\bf{\pink{Curved\:surface\:area\:=2πrh}}}$

⠀⠀

Where,

⠀⠀

r = radius of the cylinder

h = height of the cylinder

π = 22/7

⠀⠀

According to the question,

⠀⠀

⠀⠀⠀⠀⠀$\sf{:\implies 2πrh=100}$

⠀⠀

⠀⠀⠀⠀⠀$\sf{:\implies 2×\dfrac{22}{7}×10×h=100}$

⠀⠀

⠀⠀⠀⠀⠀$\sf{:\implies h=\dfrac{100×7}{22×10×2}}$

⠀⠀

⠀⠀⠀⠀⠀$\sf{:\implies h=\dfrac{700}{440}}$

⠀⠀

⠀⠀⠀⠀⠀$\sf{:\implies h={\cancel{\dfrac{700}{440}}}}$

⠀⠀

⠀⠀⠀⠀⠀$\sf{:\implies h=\dfrac{35}{22}}$

⠀⠀

⠀⠀⠀⠀⠀$\boxed{\bf{\purple{:⟹\:h\:=1.6\:cm}}}$

⠀⠀

.°. height of the cylinder is 1.6 cm

⠀⠀

We also know that,

⠀⠀

⠀⠀⠀$\boxed{\bf{\pink{Volume\:of\:cylinder\:=πr^{2}h}}}$

⠀⠀

$\sf{:\implies Volume\:of\:the\:cylinder=πr^{2}h}$

⠀⠀

$\sf{:\implies Volume\:of\:the\:cylinder=\dfrac{22}{7}×(10)^{2}×1.6\:cm^{3}}$

⠀⠀

$\sf{:\implies Volume\:of\:the\:cylinder=\dfrac{22}{7}×10×10×1.6\:cm^{3}}$

⠀⠀

$\sf{:\implies Volume\:of\:the\:cylinder=502.9\:cm^{3}}$

⠀⠀

Therefore,

Volume of the cylinder is 502.9 cm³

⠀⠀

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