A city is planning to replace one of its water storage tanks with a larger one. The city's old tank is a circular night with a radius of 12 feet and a volume of 10,000 cubic feet. The new tank is a right circular cylinder with a radius of 15 feet and the same height as the old tank. What is the maximum number of cubic feet of water in the new storage tank will hold?

Answer: 15,625 ft³Step-by-step explanation: You need to use the formula for calculate the volume of  a cylinder: [tex]V=r^2h\pi[/tex] Where r is the radius and h is the height. You know the radius and the volume of the old tank, therefore you can find the height as following: [tex]10,000=(12)^2h\pi\\\\h=\frac{10,000}{(144)\pi}ft[/tex] You know that the radius of the new tank is 15 feet and it has the same height as the old tank. Therefore, you can substitute h into the first equation for calculate the volume of a cylinder, to find the maximum number of cubic feet of water that the new storage tank will hold: [tex]V=(15ft)^2(\frac{10,000}{(144)\pi}ft)\pi=15,625ft^3[/tex]