Question

The volume of a cylinder is 352cm^3 and its height is 7cm. Find its curved surface area. (use pi = 22/7)​

Answer 1

Answer:

answer radius(r) =4 cm diameter 8 cm

Answer 2

Given :

• Volume of cylinder = 352 cm³
• Height of the cylinder = 7 cm

To find :

• Curved surface area of cylinder

Concept :

Firstly, we will find the radius of the cylinder by using the formula of volume of cylinder. Then by substituting the values in the formula of curved surface area of cylinder we will get our required answer.

→ Formula of volume of cylinder :-

$\boxed{\sf \pmb{Volume \: \: of \: \: cylinder = \pi r^2 h}}$

→ Formula of curved surface area of cylinder :-

$\boxed{\sf \pmb{ Curved \: \: surface \: \: area \: \: = 2 \pi rh}}$

where,

• Take π = 22/7
• r = radius of cylinder
• h = height of cylinder

Solution :

Radius of cylinder :-

$\\ \dashrightarrow \sf \quad Volume \: \: of \: \: cylinder = \pi r^2 h$

$\\ \dashrightarrow \sf \quad 352= \dfrac{22}{7} \times r^2 \times 7$

$\\ \dashrightarrow \sf \quad 352= \dfrac{22}{ \not7} \times r^2 \times \not7$

$\\ \dashrightarrow \sf \quad 352= 22 \times r^2$

Transposing 22 to the other side.

$\\ \dashrightarrow \sf \quad \dfrac{352}{22}= r^2$

$\\ \dashrightarrow \sf \quad \dfrac{176}{11} = r^2$

$\\ \dashrightarrow \sf \quad 16 = r^2$

Taking square root on both sides.

$\\ \dashrightarrow \sf \quad \sqrt16= r$

$\\ \dashrightarrow \sf \quad \sqrt{4 \times 4}= r$

$\\ \dashrightarrow \sf \quad \pm \: 4 \: Reject \: - ve \: = r$

$\\ \dashrightarrow \sf \quad 4 = r$

Radius of cylinder = 4 cm

Curved surface area of cylinder :-

$\\ \dashrightarrow \quad\sf Curved \: \: surface \: \: area \: \: = 2 \pi rh$

$\\ \dashrightarrow \quad\sf Curved \: \: surface \: \: area \: \: = 2 \times \dfrac{22}{7} \times 4 \times 7$

$\\ \dashrightarrow \quad\sf Curved \: \: surface \: \: area \: \: = 2 \times \dfrac{22}{ \not7} \times 4 \times \not7$

$\\ \dashrightarrow \quad\sf Curved \: \: surface \: \: area \: \: = 2 \times 22 \times 4$

$\\ \dashrightarrow \quad\sf Curved \: \: surface \: \: area \: \: = 176$

$\\ \star \quad\sf \blue{Curved \: \: surface \: \: area \: \: of \: \: cylinder \: = 176 \: {cm}^{2} }$

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~Know More :

$\leadsto \tt Surface ~~area~~ of~~ sphere = 4 \pi r^2$

$\leadsto \tt Volume of cone = \dfrac{1}{3} \pi r^2h$

$\leadsto \tt Curved ~~surface~~ area ~~of~~ cone = \pi rl$

$\leadsto \tt Total ~~surface~~ area ~~of ~~cone~~ = \pi rl + \pi r^2h$

$\leadsto \tt Total~~ surface ~~area~~ of~~ cylinder = 2 \pi rh + 2 \pi r^2$

$\leadsto \tt Area~~ of~~ circle = \pi r^2$

$\leadsto \tt Diameter = 2 \times Radius$