Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour

A right circular cylinder just encloses a sphere of radius r (see Fig). Find
i) surface area of the sphere
ii) curved surface area of the cylinder
iii) ratio of the areas obtained in i) and ii).


Answer :

image

i) Surface area of sphere = \(4 {\pi} {r}^2\)

ii) Height of cylinder = r + r = 2r
Radius of cylinder = r
We know that,

CSA of cylinder
= \(2{\pi}rh\)
= \(2{\pi}r(2h)\)
= \(4{\pi} {r}^2\)


iii) ratio of the areas obtained
= \(\frac{Surface area of sphere}{CSA of cylinder}\)
= \(\frac{4 {\pi} {r}^2}{4 {\pi} {r}^2}\)
= \(\frac{1}{1}\)

Therefore, the ratio between these two surface areas is 1:1.

NCERT solutions of related questions for Surface areas and volumes

NCERT solutions of related chapters class 9 maths

NCERT solutions of related chapters class 9 science