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

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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

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:

$\star\:\:\:\bf{Given}⋆$

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

height = 6 cm

$\star\:\:\:\bf{To\:find}⋆$

Find the areas of its total surface and lateral curved surface

$\star\:\:\:\bf{Solution}⋆$

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,

$\sf{\implies πr^{2}h=150}$

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