Question

If the radius and the height of a circular cylinder are 10 cm and 15 cm, respectively, and the radius of a sphere is 5 cm, then what is the ratio of the curved surface area of the cylinder to that of the sphere?

• A. 3 : 2
• B. 5 : 1
• C. 3 : 1
• D. 1 : 3

Answer 1

Answer:

C. 3 : 1

Shortcut Trick 

2πrh : 4πr²

⇒ rh : 2r²

⇒ 10 x 15 : 2 x 5²

⇒ 3 : 1 

∴ Required ratio is 3 : 1.

Alternate Method

Given:

Radius of cylinder = 10 cm

Height of cylinder = 15 cm

Radius of sphere = 5 cm

Formula used:

Curved surface area of cylinder = 2πrh

Surface area of sphere = 4πr²

Calculation:

According to question,

⇒ 2πrh : 4πr2

⇒ rh : 2r2

⇒ 10 x 15 : 2 x 52

⇒ 3 : 1 

∴ Required ratio is 3 : 1.

Additional Information

Volume of cylinder = πr²h

Curved surface area of cylinder = 2πrh

Total surface are of cylinder = 2πr (h + r)

Volume of sphere = 4πr³/3

Surface area of sphere = 4πr²