Question

The ratio of the volume of two spheres is 8:27. If r and R are the radii of the spheres respectively, then find the (R-r). If R=3cm, find r.

Answer 1

Answer:

R-r =1  and r=2

Step-by-step explanation:

Given r,R are the radii of the spheres respectively

Given Ratios of volumes of two sphere are 8:27

We know the formula of volume of sphere is V=$4/3[\pi r^{3} ]$

So We get,

$\frac{\frac{4}{3}\left[\pi r^3\right]}{\frac{4}{3}\left[\pi R^3\right]}=\frac{8}{27}$

hence

$\frac{\:r^3}{\:R^3}=\frac{8}{27}$

$\\\frac{\:r}{\:R}=\frac{2}{3}\\if\:R=3\:then\:r=\frac{2}{3}R\\\\\:r=2$

Hence R-r=3-2=1

and r=2

Answer 2

Answer:

R-r = 3-2 =1

If R = 3 cm then r = 2

Step-by-step explanation:

Formula:-

Volume of sphere =4/3 πr³

where r is the radius of sphere.

It is given that,

The ratio of the volume of two spheres is 8:27. If r and R are the radii of the spheres respectively

To find R and r

Let v₁ and v₂ be the volume of 2 spheres

v₁/v₂ = 8/27

$\frac{4/3pir^{3}}{4/3piR^{3}}=8/27$

$\frac{r^{3}}{R^{3}}=8/27$

$\frac{r}{R}=2/3$

Therefore R = 3 and r = 2

To find R-r

R = 3 and r = 2

R - r = 3- 2 = 1

If R=3cm find r

$\frac{r}{R}=2/3$

$\frac{r}{3}=2/3$

r = 2