Your city council has decided to build a cone shaped reservoir. The plan that was given to the building contractor indicated that the top diameter of the reservoir must be 50m. The depth of the reservoir is indicated at 30m. 1. What volume of water can be stored in the reservoir? II. What is the surface area of the wall of the cone?

Question I: What volume of water can be stored in the reservoir? Step 1: Formula for the volume of a cone. V = (1)/(3) r^2 h Top diameter = 50 m, so radius r = 25 m. Depth h = 30 m. Step 2: Substitute the values. V &= (1)/(3) (25)^2 (30) \\ &= (1)/(3) (625) (30) \\ &= (1)/(3) (18750) \\ &= 6250 Volume = 6250 m³. 6250 m^3 Question II: What is the surface area of the wall of the cone? Step 1: Slant height l. l &= sqrt(r^2) + h^2 \\ &= sqrt(25^2) + 30^2 \\ &= sqrt(625 + 900) \\ &= sqrt(1525) \\ &= sqrt(25 × 61) \\ &= 5sqrt(61) Slant height = 5sqrt(61) m. Step 2: Lateral surface area of the cone. A = r l A &= (25) (5sqrt(61)) \\ &= 125 sqrt(61) Surface area = 125 sqrt(61) m². 125(61) m^2