Question

A hollow spherical iron shell floats almost completely submerged in water. The outer diameter is 60.0 cm, and the density of iron is 7.87 g∕c m cubed . Find the inner diameter in cm. Express to 3 sig figs.

Answer 1

The inner diameter is 57.3 cm

Step-by-step explanation:

The inner diameter of the hollow spherical iron shell can be found using the weight of the sphere (
`W_(s)`) and the weight of the water displaced (
`W_(w)`):

`W_(s) = W_(w)`

`m_(s)*g = m_(w)*g`

`D_(s)*V_(s) = D_(w)*V_(w)`

Where D is the density and V is the volume

`D_(s)*(4)/(3)\pi*((d_(o)^(3) - d_(i)^(3))/(2^(3))) = (4)/(3)\pi*((d_(o))/(2))^(3)`

Where
`d_(o)` is the outer diameter and
`d_(i)` is the inner diameter

`D_(s)*(d_(o)^(3) - d_(i)^(3)) = d_(o)^(3)`

`D_(s)*d_(i)^(3) = d_(o)^(3)(D_(s) - 1)`

`7.87*d_(i)^(3) = 60.0^(3)(7.87 - 1)`

`d_(i) = 57.3 cm`

Therefore, the inner diameter is 57.3 cm.

I hope it helps you!