A Spherical Ice ball is melting such that the radius is decreasing at a constant rate of 0.1 cm/s

A Spherical Ice ball is melting such that the radius is decreasing at a constant rate of 0.1 cm/s Find the amount of water Formed in one second When the radius of Sphere is 7 cm(specific gravity of ice is 0.9)


thanks

one divided by infinite

any operatoion perfoming in=ncludedinfinitr=ev is clalled indeterminate form

First, I should note that specific gravity is a relation between the density of a substance and the density of a reference. Unless they specifically say that the reference is water, the question is flawed.

On to the actual solution: The easiest way to do this is to find the volume of the sphere (4/3*pi*r^3) with a radius of 7 cm. Then, if it melts for one second at a rate of 0.1 cm/s, then find the volume of the sphere with a radius of 6.9 cm.

If you take the difference in volume, that is how much ice has melted. Because ice is less dense than water, the final volume of water must be smaller than the volume of ice, so you multiply by 0.9, the estimation for the density of ice in this problem, to find how much water.

pretty easy

the volume of ice at t (time) = 0s
V_0=4/3*Pi*r³ with r=7cm
V_0=1437 cm³
at time t=1s, the radius of the sphere is decreased by 0.1cm
so V_1=4/3*Pi*(r-0.1)³ = 1376cm³

That a decrease of 60cm³ of ice
And because of water is denser than ice we have to multiply the volume of molten ice by 0.9
so the amount of water formed is 60cm³*0.9= 54cm³

Here you go ;)

You should ask for your teacher it's diffcult