Definite Integration Question 306
Question: A frustum of sphere is made by cutting two parallel planes of any sphere. If radius of sphere is 5 cm and distance between the plane is 1 cm, then what will be the curved surface of frustum when the distance of first plane from the centre of sphere is 2 cm
[UPSEAT 1999]
Options:
A) $ 5\pi cm^{2} $
B) $ 10\pi cm^{2} $
C) $ 15\pi cm^{2} $
D) $ 40\pi cm^{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
Equation of circle is, $ x^{2}+y^{2}=5^{2} $
$ \therefore y^{2}=25-x^{2} $ , $ 2y\frac{dy}{dx}=-2x $ ,
$ \therefore \frac{dy}{dx}=-\frac{x}{y} $ Curved surface of frustum $ =2\pi \int_2^{3}{yds} $
$ =2\pi \int_2^{3}{y.\frac{5}{y}dx} $
$ =2\pi \int_2^{3}{5dx} $
$ =2\pi [5x]_2^{3}=10\pi cm^{2} $ .
BETA
