A water tank has the shape of a right circular cone, with the height of 16 feet and a radius of 8 feet. Water is running into the tank so that the radius r of the surface at any given t (time) is given by r(t) = 1.5t , where t is the time (in minutes) that the water has been running.

a. The area of the surface of the water is A=(pi)r^2 . find A(t) . Use it to determine the area of the surface of the water when t = 2.

b. The volume of the water is given by V = 1/3 (pi) r^2 h . Use it to determine the volume of the water when
t=3 minutes.

Question

A water tank has the shape of a right circular cone, with the height of 16 feet and a radius of 8 feet. Water is running into the tank so that the radius r of the surface at any given t (time) is given by r(t) = 1.5t , where t is the time (in minutes) that the water has been running.

a. The area of the surface of the water is A=(pi)r^2 . find A(t) . Use it to determine the area of the surface of the water when t = 2.

b. The volume of the water is given by V = 1/3 (pi) r^2 h . Use it to determine the volume of the water when 
t=3 minutes.