# .The height of a cylinder is 15cm and the curved surface area is 660 cm2. Find its radius, total surface a

.The height of a cylinder is 15cm and the curved surface area is 660 cm2

surface area and volume.​

1. ### Given :

• Height of a cylinder = 15 cm
• Curved surface area = 660 cm²

### Tofind :

• Total surface area of cylinder
• Volume of the cylinder

### ConceptUsed :

→ Formula of Curved surface of cylinder :-

• CSA of cylinder = 2πrh

→ Formula of Total surface area of cylinder :-

• TSA of cylinder = 2πr(h + r)

→ Formula of volume of cylinder :-

• Volume = πr²h

where,

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

### Solution:

⠀⠀⠀⇒ CSA of cylinder = 2πrh

⠀⠀⠀⇒ 660 = 2 × 22/7 × r × 15

⠀⠀⠀⇒ 660 = 660/7 × r

⠀⠀⠀⇒ 660 × 7/660 = r

⠀⠀⠀⇒ 7 = r

Radius of the cylinder = 7 cm

TSA of cylinder →

⠀⠀⠀⇒ TSA of cylinder = 2πr(h + r)

⠀⠀⠀⇒ TSA = 2 × 22/7 × 7(15 + 7)

⠀⠀⠀⇒ TSA = 2 × 22(22)

⠀⠀⠀⇒ TSA = 968

Total surface area of cylinder = 968 cm²

Volume of cylinder →

⠀⠀⠀⇒ Volume = πr²h

⠀⠀⠀⇒ Volume = 22/7 × (7)² × 15

⠀⠀⠀⇒ Volume = 22/7 × 7 × 7 × 15

⠀⠀⠀⇒ Volume = 22 × 7 × 15

⠀⠀⠀⇒ Volume = 2310

Volume of cylinder = 2310 cm³

Using the formula

A=2πrh+2πr2

Solving forr

r=1

2h2+2A

π﹣h

2=1

2·152+2·660

π﹣15