Finding the volume of a composites figure is like finding the volume of each individual solid figure. These individual solid figures such as prisms, cylinders, pyramids, cones, and spheres are combined to make three dimensional solids called composites figures.

Let's return to our example of the water tower.

The figure represents the water tower for a local town. Climatologists are forecasting a drought, and the mayor of the town wants to know how much water the water tower can hold when it is completely full. Determine the volume of water that the full water tower can hold.

1. Identify the Interactive popup. Assistance may be required. 3-dimensional solids This figure is a cone and a cylinder. present in the figure of which you know how to find the volume.
2. Determine the volume of the cone. Identify the Interactive popup. Assistance may be required. formula V = 1 3 πr²h for the volume of the cone. Do you have all of the Interactive popup. Assistance may be required. dimensions?

   We are given the slant height and the radius of the cone, but we need to know the altitude height of the cone. Let's use the Pythagorean Theorem to determine it!

   a² + b² = c²
   h² + 16² = 20²
   h² + 256 = 400
   h² = 144
   h = √144 = 12 feet
   
   Now, you can find the Interactive popup. Assistance may be required. volume of the cone V = 1 3 πr²h
   = 1 3 π (16 feet)² (12 feet)
   ≈ 3215 ft³ .
3. Determine the volume of the cylinder. Identify the Interactive popup. Assistance may be required. formula V = πr²h Do you have all of the Interactive popup. Assistance may be required. dimensions? Yes, we know both the radius and the height. Find the Interactive popup. Assistance may be required. volume of the cylinder V = πr²h
   = π(16 feet)²(30 feet)
   ≈ 24,115 ft³ .
4. Find the Interactive popup. Assistance may be required. sum of the volumes V_total = V_cone + V_cylinder
   ≈ 3,215 ft³ + 24,115 ft³
   ≈ 27,330 ft³ .