Question

Question - The total surface surface area of a cylinder of diameter 14 cm and 836 cm '2 find volume of cylinder ????

For Genius

Answer 1

Given,

• Diameter of the cylinder = 14 cm

• Radius of the cylinder = $\bold{\frac{14}{2} = 7 \ cm}$

• Total surface area of cylinder = 836 cm²

To Find ,

• Volume of the Cylinder = ?

Solution,

Supoose the height of the cylinder be h cm

We know that :

$\boxed{\bold{\red{T.S.A = 2\pi r (h +r) = 836}}}$

$\implies \bold{2 \times \frac{22}{7} \times 7 (h + 7) = 836}$

$\implies \bold{44(h + 7) = 836}$

$\implies \bold{h + 7 = \frac{836}{44}}$

$\implies \bold{h + 7 = 19}$

$\implies \bold{h = 19 - 7}$

$\implies \boxed{\bold{ h = 12 \ cm}}$

Now Find Volume of Cylinder :

$\implies \boxed{\bold{ Volume \ of \ the \ Cylinder = \pi r^{2} h}}}$

$\implies \bold{\frac{22}{7} \times (7)^{2} \times 12}$

$\implies \bold{ 22 \times 7 \times 12}$

$\implies \boxed{\bold{1848 \ cm^{3}}}$

Therefore,

Volume of Cylinder = 1848 cm³(Answer)

$\rule{200}2$

Answer 2

$\large{\underline{\underline{\bold{\red{\sf{Question}}}}}}$

The total surface surface area of a cylinder of diameter 14 cm and 836 cm '2 find volume of cylinder ????

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\large{\underline{\underline{\bold{\blue{\sf{Solution}}}}}}$

Diamater → 14cm.

Radius→$\dfrac{14}{2}↦7cm$

Total Surface .Area of Cylinder→836cm²

$2 π r(r + h) →836cm$

Putting Values:.

$2\times\dfrac{22}{7}×7\times{(7+h)}→836cm$

⟹44 + (7+h) →836cm²

⟹7+h →$\cancel\dfrac{836}{44}→19cm$

⟹h = 19 - 7

⟹$\large{\underline{\underline{\bold{\green{\sf{H = 12cm}}}}}}$

Now we have to find the volume of Cylinder:.

Volume of Cylinder → π r²h

Putting Values:.

$\dfrac{22}{7}\times{7}\times{7}\times{12}$

$→<strong>22×7×12</strong>$

$\large{\underline{\underline{\bold{\orange{\sf{Answer:{1848cm}^{3}}}}}}}$