Question

the ratio of volumes of two spheres is 64:27find the ratio of there surface area

Answer 1

Step-by-step explanation:

volume of sphere=4/3πr^3

ratio=r^3/R^3=64/27

r/R=4/3

surface area=4πr^2

r^2/R^2=16/9

Answer 2

Solution

Let Radius of first sphere be "r" and radius of second sphere is "s"

So According to the question

$\frac{ \frac{4}{3}\pi {r}^{3} }{ \frac{4}{3} \pi {s}^{3} } = \frac{64}{27} \\ \\ \frac{ {r}^{3} }{ {s}^{3} } = \frac{ {4}^{3} }{ {3}^{3} } \\ \\ \frac{r}{s} = \frac{4}{3} \\ \\ therefore .......\: r \: = 4 \: and \: s = 3$
Now the ratio of Surface Area of Spheres ---

$\frac{4\pi {r}^{2} }{4\pi {s}^{2} } \\ \\ = \frac{ {r}^{2} }{ {s}^{2} } \\ \\ = \frac{ {4}^{2} }{ {3}^{2} } \\ \\ = \frac{16}{9}$

= 16 : 9 is the ratio of the spheres.