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Sanjana Katial

· started a discussion

· 1 Months ago

Ratio (Question: 163809.0 )

Ratio of surface area is 2:3

Question:
A right circular cylinder and a sphere have same radius and same volume. The ratio of their surface area is:
Options:
A) 2: 1
B) 1:6
C) 1: 1
D) 7 : 6
Solution:

Volume of cylinder = Volume of sphere

⇒ πr2h = \(\cfrac{4}{3}\)  πr3,

⇒ \(\cfrac{h}{r}\) = \(\cfrac{4}{3}\)

∴ \(\cfrac{Surface area of cylinder}{Surface area of sphere}\)

⇒ \(\cfrac{2πrh + 2πr^2}{4πr^2}\) = \(\cfrac{2πrh}{4πr^2}\) + \(\cfrac{2πr^2}{4πr^2}\)

= \(\cfrac{h}{2r}\) + \(\cfrac{1}{2}\) = \(\cfrac{4}{6}\) + \(\cfrac{1}{2}\) = \(\cfrac{7}{6}\)


Knowledge Expert

· commented

· 1 Months ago

Dear Student,
7:6 is the required ratio...
Here, you need to apply TSA(Total Surface Area of Cylinder and Sphere).........not CSA....
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