Question

4. If the lateral surface of a cylinder is 94.2 cm- and its height is 5 cm, then
(i) radius of its base (ii) its volume. (Use it = 3.14)​

Answer 1

Given :

• Height (h) = 5 cm

• Lateral surface = 95.2 cm²

______________________

Solution :

(i) Radius of cylinder :

Let the radius of cylinder be r cm

______________________

According to question now :

CSA of cylinder = 2πrh

2πrh = 95.2 cm²

2 × 3.14 × r × 5 = 95.2

10 × 3.14 × r = 95.2

r = 95.2/10 × 3.14

r = 3 cm

.....---------------------------------.....

(ii) Volume of cylinder :

Volume of cylinder = πr²h

Volume of cylinder = 3.14 × (3)² × 5

Volume of cylinder = 141.3 cm³

Answer 2

☆ To Find :

$\bullet$ The Radius of the Cylinder.

$\bullet$ The Volume of the Cylinder.

☆ Given :

• Curved surface area of the Cylinder = 94.2 cm².

• Height of the Cylinder = 5 cm

☆ We Know :

☞ Lateral surface area of a Cylinder :

$\green{\sf{\underline{\boxed{CSA = 2\pi rh}}}}$

Where,

• r = Radius of the Circle

• h = Height of the Cylinder

• CSA = Curved surface area of the Cylinder.

☞ Volume of the Cylinder :

$\green{\sf{\underline{\boxed{V = \pi r^{2}h}}}}$

Where ,

• r = Radius of the Circle

• h = Height of the Cylinder

• CSA = Curved surface area of the Cylinder.

☆ Concept :

Since , the Curved surface area and the height is given we can find the radius.

And after finding the Radius , we can use the formula for Volume of a Cylinder , to determine it's value.

☆ Solution :

☞ Radius of the Circle :

• CSA = 94.2 cm²

• Height = 5 cm

• π = 3.14

Let the Radius be r cm.

Using the formula for curved surface area of a Cylinder and substituting the values in it , we get :

$\purple{\bigstar\:\sf{CSA = 2\pi rh}\:\bigstar} \\ \\ \\ \implies \sf{94.2 = 2 \times 3.14 \times r \times 5} \\ \\ \\ \implies \sf{94.2 = 6.28 \times 5 r} \\ \\ \\ \implies \sf{94.2 = 31.4 r} \\ \\ \\ \implies \sf{\dfrac{\cancel{94.2}}{\cancel{31.4}} = r} \\ \\ \\ \implies \sf{3 cm = r} \\ \\ \\ \therefore \purple{\sf{3 cm = r}}$

Hence , the Radius of the Cylinder is 3 cm.

☞ Volume of the Cylinder :

• Radius = 3 cm

• Height = 5 cm

Using the formula for Volume of the Cylinder , and Substituting the values in it , we get :

$\purple{\bigstar\:\sf{V = \pi r^{2}h}\:\bigstar} \\ \\ \\ \implies \sf{V = 3.14 \times 3^{2} \times 5} \\ \\ \\ \implies \sf{V = 3.14 \times 9 \times 5} \\ \\ \\ \implies \sf{V = 3.14 \times 45} \\ \\ \\ \implies \sf{V = 141.3 cm^{3}} \\ \\ \\ \therefore \purple{\sf{V = 141.3 cm^{3}}}$

Hence , the volume of the Cylinder is 141.3 cm³.

☆ Answer :

• Radius of the Cylinder = 3 cm.

• Volume of the Cylinder = 141.3 cm³.

☆ Additional information :

• Total Surface Area of a Cylinder : 2πr(h + r)

• Volume of a Cube = a³

• Volume of a Sphere = 4/3 πr³