Question

Feb 18, 2014 · The ratio of the radii of two spheres is 1:2. The two sphere are melted together to form a cylinder of height which is 12 times its radius.what is the ratio of the radius of the smaller sphere and the cylinder

Answer 1

is it right I am not confirm

Answer 2

Answer:

The ratio of the radius of the smaller sphere and the cylinder is 1:1

Step-by-step explanation:

Given that the ratio of the radii of two spheres is 1:2. The two sphere are melted together to form a cylinder of height which is 12 times its radius.

we have to find the ratio of the radius of the smaller sphere and the cylinder.

$\text{Let the radius of two spheres are }r_1\text{ and }r_2$

The ratio of the radii of two spheres is 1:2

⇒ $r_1:r_2=1:2$

$\frac{r_1}{r_2}=\frac{1}{2}$

$r_2=2r_1$

Let the radius of cylinder is R and therefore acc to question height is 12 R

The two sphere are melted together to form a cylinder of height which is 12 times its radius.

Hence, the volume are equal

$\text{Volume of two spheres=Volume of cylinder}$

$\frac{4}{3}\pi (r_1)^3+\frac{4}{3}\pi (r_2)^3=\pi R^2h$

$\frac{4}{3}\pi[(r_1)^3+(r_2)^3]=\pi R^2\times 12R$

$\frac{4}{3}\pi[(r_1)^3+(2r_1)^3]=12\pi R^3$

$\frac{4}{3}\pi[(r_1)^3+8(r_1)^3]=12\pi R^3$

$\frac{4}{3}\pi[9(r_1)^3]=12\pi R^3$

$12\pi (r_1)^3=12\pi R^3$

$\frac{(r_1)^3}{R^3}=1$

$\frac{r_1}{R}=1$

Hence, the ratio of the radius of the smaller sphere and the cylinder is 1:1