Question

The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the diameter is 80 mm?

Answer 1

Explanation:

volume of sphere v=4/3 π r³

`(dv)/(dt) =(4)/(3) *3 \pi r2 * (dr)/(dt) \\(dv)/(dt) =4 \pi r^2 (dr)/(dt) \\given ~(dr)/(dt) =2 ~mm/s\\when ~diameter=80~mm\\radius=(80)/(2)=40~mm\\(dv)/(dt) =4\pi (40)^2 * 2=12800~mm^3`