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

6.99 cm

Step-by-step explanation:

Mass of any sphere is defined by the formula,

`m=V* \rho`

Here, V is thew volume of sphere whose value is
`(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)=(4)/(3)\pi r_(1) ^(3)\rho`

Now mass of sphere 2

`m_(2)=(4)/(3)\pi r_(2) ^(3)\rho`

Now according to question.

`m_(2)=3m_(1)`

Put the values

`(4)/(3)\pi r_(2) ^(3)\rho=3 (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.