The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 mm

Question

asked Feb 17, 2022 19.9k views

1 Answer

Joncham · Answer 1 · 2022-02-24T15:23:42+0000

Answer:

$(dV)/(dt)=502.65\ mm^3/s$

Explanation:

The volume of a sphere is given by :

$V=(4)/(3)\pi r^3$

The rate of change of volume means,

$(dV)/(dt)=(d)/(dt)((4)/(3)\pi r^3)\\\\(dV)/(dt)=(4)/(3)\pi * 3r* (dr)/(dt)$

We have,
$(dr)/(dt)=2\ mm/s\ and\ r=40\ mm$

So,

$(dV)/(dt)=(4)/(3)\pi * 3* 20* 2\\\\=502.65\ mm^3/s$

So, the volume is increasing at the rate of
$502.65\ mm^3/s$ .