Question

The volume of one sphere is 27 times that of the another sphere calculate the ratio of their radii, surface area

Answer 1

given

volume of big sphere = 27 × volume of small sphere

4/3 π R^3 = 27 × 4/3 π r^3

R^3 = 27 × r^3

R^3 / r^3 = 27 / 1

taking cube root of both sides

R / r = 3 / 1

ie R : r = 3 : 1

Answer 2

Answer:

Step-by-step explanation:

Let the radius of one sphere be=R and the radius of the another sphere be= r, then according to question, we have

The volume of one sphere = 27 times that of the another sphere

$\frac{4}{3}{\times}{\pi}R^{3}=\frac{4}{3}{\times}{\pi}r^{3}$

$R^{3}=27r^{3}$

$\frac{R^{3}}{r^{3}}=\frac{27}{1}$

$\frac{R}{r}=\frac{3}{1}$

Hence, the ratio of their radii is:$\frac{R}{r}=\frac{3}{1}$

Now, Surface area of the sphere having radius R=$4{\pi}R^{2}=4{\pi}(3)^{2}=113.04sq units$.

And surface area of the sphere having radius r=$4{\pi}r^{2}=4{\pi}(1)^{2}=12.56sq units$