Question

Two spheres are cut from a certain uniform rock, One has radius 4.85 cm. The mass of the other is three times greater. Find its radius.

Answer 1

Answer:

6.99 cm

Explanation:

Mass of any sphere is defined by the formula,

$m=V\times \rho$

Here, V is thew volume of sphere whose value is $\frac{4}{3}\pi r^{3}$, m is the mass, $\rho$ is the density.

So according to the question two spheres are cut from same material means they have same density.

And mass of other sphere is 3 times mass of one and the radius of sphere 1 is 4.85 cm.

$m_{2}=3 m_{1}$

Now mass of sphere 1.

$m_{1}=\frac{4}{3}\pi r_{1} ^{3}\rho$

Now mass of sphere 2

$m_{2}=\frac{4}{3}\pi r_{2} ^{3}\rho$

Now according to question.

$m_{2}=3m_{1}$

Put the values

$\frac{4}{3}\pi r_{2} ^{3}\rho=3 \frac{4}{3}\pi r_{1} ^{3}\rho\\r_{2} ^{3}=3 r_{1} ^{3}\\r_{2} ^{3}=3(4.85)^{3} \\r_{2} ^{3}=342.252375\\r_{2}=6.99 cm$

Therefore, radius of other sphere is 6.99 cm.