Question

the volume of a cylindrical of the is 150 pie cm³. and its height is 6 cm . Find the areas of its total surface and lateral curved surface ?. ​

Answer 1

Question:

the volume of a cylindrical of the is 150 pie cm³. and its height is 6 cm . Find the areas of its total surface and lateral curved surface

Answer:

$\star\:\:\:\bf\large\underline\red{Given}$

the volume of a cylindrical of the is 150 pie cm³.

its height is 6 cm

$\star\:\:\:\bf\large\underline\red{To\:find}$

Find the areas of its total surface and lateral curved surface

$\star\:\:\:\bf\large\underline\red{Solution}$

Volume of cylinder = 150π cm³

As wwe know that volume of the cylinder is given as-

$\boxed{\bf{\blue{V=πr^{2}h}}}$

Where,

V = Volume of the cylinder

r = Radius of the cylinder

h = height of the cylinder

ATQ,

$\sf{\implies πr^{2}h=150}$

$\sf{\implies r^{2}=\dfrac{150}{6}}$

$\sf{\implies r=\sqrt{25}}$

$\sf{\implies r=5}$

We also know that,

$\boxed{\bf{\green{Lateral\:surface\:area\:of\:cylinder=2πrh}}}$

.°. Lateral surface area of the cylinder

= 2πrh

= 2 × π × 5 × 6 cm²

= 60 π cm²

Now,

$\boxed{\bf{\purple{Total\:surface\:area\:of\:cylinder=2πr(r+h)}}}$

Therefore,

Total surface area of the cylinder

= 2πr(r+h)

= 2 × π × 5 × (5 + 6) cm²

= 110π cm²

Therefore,

lateral curved surface of the cylinder is 60 cm² and

Total surface area of the cylinder is 110π cm²

______________________________

Answer 2

Answer:

Question:

the volume of a cylindrical of the is 150 pie cm³. and its height is 6 cm . Find the areas of its total surface and lateral curved surface

Answer:

\star\:\:\:\bf\large\underline\red{Given}⋆

Given

the volume of a cylindrical of the is 150 pie cm³.

its height is 6 cm

\star\:\:\:\bf\large\underline\red{To\:find}⋆

Tofind

Find the areas of its total surface and lateral curved surface

\star\:\:\:\bf\large\underline\red{Solution}⋆

Solution

Volume of cylinder = 150π cm³

As wwe know that volume of the cylinder is given as-

\boxed{\bf{\blue{V=πr^{2}h}}}

V=πr

2

h

Where,

V = Volume of the cylinder

r = Radius of the cylinder

h = height of the cylinder

ATQ,

\sf{\implies πr^{2}h=150}⟹πr

2

h=150

\sf{\implies r^{2}=\dfrac{150}{6}}⟹r

2

=

6

150

\sf{\implies r=\sqrt{25}}⟹r=

25

\sf{\implies r=5}⟹r=5

We also know that,

Step-by-step explanation:

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