Question

the volume of a right circular cylinder is 38016cm3.if the height of the cylinder is 21cm, find it curves surface area?​

Answer 1

Question:

The volume of a Right circular Cylinder is 38016cm³. If the Height of the Cylinder is 21cm, Find it curved surface area.

Given:

• Volume of Right Circular Cylinder is 38016cm³.
• Height of Cylinder is 21cm.

To Find:

• Curved Surface area of Cylinder.

Concept:

Here, the concept of Surface Areas and Volume is used. We are given with Height and volume of Right circular cylinder. We have to find it's Curved Surface area. To find it's Curved Surface area, Firstly find the radius of cylinder and then equating values in Formula of Curved surface area of cylinder.

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★ Formula Used:

$\mapsto\mathsf{Volume\: of\: Cylinder=\pi{r}^{2}h}$

$\mapsto\mathsf{CSA\: of\: Cylinder=2\pi rh}$

• r is Radius of cylinder
• h is Height of Cylinder

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Solution:

Let's Firstly find out the radius of cylinder by equating values of cylinder in Volume of cylinder Formula.

$\rightarrow\mathsf{Volume\: of\: cylinder=\pi{r}^{2}h}$

Substituting all values of Cylinder in Formula;;

$\rightarrow\mathsf{38016=\pi\times {r}^{2}\times 21}$

Equating value of π as $\mathsf{\large\frac{22}{7}}$

$\rightarrow\mathsf{38016=\large{\frac{22}{7}}{r}^{2}\times 21}$

Now, Dividing 21 by 7.

$\rightarrow\mathsf{38016=22\times 3\times {r}^{2}}$

$\rightarrow\mathsf{38016=66\times {r}^{2}}$

Now, Dividing 38016 by 66.

$\rightarrow\mathsf{\large{\frac{38016}{66}}={r}^{2}}$

$\rightarrow\mathsf{576={r}^{2}}$

Taking square root of 576;;

$\rightarrow\mathsf{{24}^{2}={r}^{2}}$

Removing square of both the side.

$\rightarrow\bold{24=r}$

Hence, the Radius of Cylinder is 24cm.

Now, Let's substitute all values in Formula of CSA of Cylinder.

$\implies\mathsf{CSA\: of\: Cylinder=2\pi rh}$

$\implies\mathsf{CSA\: of\: Cylinder=2\times \pi\times 24\times 21}$

Equating value of π as $\mathsf{\large\frac{22}{7}}$ $\\ \implies\mathsf{CSA\: of\: Cylinder=2\times\large{\frac{22}{7}}\times 24\times 21}$

Now, Dividing 21 by 7.

$\implies\mathsf{CSA\: of\: Cylinder=2\times 22\times 24\times 3}$

$\implies\mathsf{CSA\: of\: Cylinder=44\times 24\times 3}$

$\implies\mathsf{CSA\: of\: Cylinder=1056\times 3}$

$\implies\bold{CSA\: of\: Cylinder=3168}$

This is the required answer.

$\underline{\boxed{\mathtt{Curved\: surface\: Area\: of\: cylinder=\color{purple}\bold{3168\: {cm}^{2}}}}}$