A solid sphere is cut into two hemisphere. The ratio of the surface areas of sphere to that of two hemisphere taken together, is

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
A solid sphere is cut into two hemisphere. The ratio of the surface areas of sphere to that of two hemisphere taken together, is:

1 1 : 1

2 1 : 4

3 2 : 3

4 3 : 2

Ans.
(3)

Let r be the radius of sphere.

$S u r f a c e a r e a o f s p h e r e = 4 π r^{2} T o t a l s u r f a c e a r e a o f e a c h h e m i s p h e r e = C u r v e d s u r f a c e a r e a = 2 π r^{2}$

$B a s e a r e a = π r^{2} Total = 2 π r^{2} + π r^{2} = 3 π r^{2} S o f o r t w o h e m i s p h e r e s :$

$3 π r^{2} + 3 π r^{2} = 6 π r^{2} R e q u i r e d r a t i o : = \frac{4 π r^{2}}{3 π r^{2} + 3 π r^{2}} = \frac{4 π r^{2}}{6 π r^{2}} = \frac{4}{6} = \frac{2}{3}$

Want Us to Email you About Special Offers & Updates?