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

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

ii) Height of cylinder = r + r = 2r
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.