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GeoGebraGeoGebra Classroom

Thinking Ahead (8.GEO.90) Optional

Hint; This task gives students an opportunity to work with volumes of cylinders, spheres and cones. Notice that the insight required increases as you move across the three glasses, from a simple application of the formula for the volume of a cylinder, to

The diagram shows three glasses (not drawn to scale). The measurements are all in centimeters.The bowl of glass 1 is cylindrical. The inside diameter is 5 cm and the inside height is 6 cm.The bowl of glass 2 is composed of a hemisphere attached to cylinder. The inside diameter of both the hemisphere and the cylinder is 6 cm. The height of the cylinder is 3 cm.The bowl of glass 3 is an inverted cone. The inside diameter is 6 cm and the inside slant height is 6 cm.

  1. Find the vertical height of the bowl of glass 3.
  2. Calculate the volume of the bowl of each of these glasses.
  3. Glass 2 is filled with water and then half the water is poured out. Find the height of the water.