Related rates problem: the radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week. the thickness of the rind is always one tenth of the radius. the volume of the rind is growing at the rate cubic centimeters per week at the end of the fifth week. assume that the radius is initially zero.

Check the picture below.

so, if we grab the whole volume of the watermelon, and then subtract the volume of the inner sphere of 9/10, what we're left with is 1/10 of the volume, which is the volume of the rind, recall the rind has a radius of 1/10 of the radius, so we're simply taking off 1/10 from the radius and using the 9/10 and subtracting the volume with that radius.

now, after the 5th week, the radius of the watermelon has then grown to 2*5, or 10 cm, and the rind is 1/10 of that or just 1 cm.

What’s the improper fraction?