Calculus- conical pile

Question

Sand is pouring out of a pipe and is forming a conical pile on the ground.The radius of the pile is increasing at a rate of 5 feet per day.The height is always 1/4 of the radius.When the pile has a radius of 13 meters,

a) the Volume is __ cubic feet

b) the rate of change of the VOLUME is __cubic feet per day

Answer 1

V=πr²h/3 formula for the volume of a cone

r' = 5'/day

h = r/4

V(13) =πr³/12 = 575.17 ft³/day

V' = 3πr²r'/12 = 3π(13)²(5)/12 = 663.66 ft³ / day