Volume of Spheres

•Starter– A cone has a diameter of 16m and a

slant height of 10m. Find the volume of the cone.

April 13, 2010

Review

Volume of Square Pyramid – Related to volume of large cube

Volume of Cone– Related to volume of cylinder

Moving on…

How can we use the same idea to find the volume of a sphere?

Materials

Hemisphere with radius rCylinder with radius r and height 2rCone with radius r and height 2rRice

Procedure

Fill the hemisphere with rice. Carefully pour the contents of the hemisphere into the cylinder. What fraction of the cylinder does the hemisphere appear to fill? Fill the hemisphere again and pour the contents into the cylinder. What fraction of the cylinder do two hemisphere appear to fill?

Procedure

If the radius of the cylinder is r and the height is 2r, then what is the volume of the cylinder in terms of r? The volume of the sphere is the fraction of the cylinder’s that was filled by two hemispheres. What is the formula for the volume of a sphere? The volume of a sphere with radius r is given by the formula: V=4/3πr 3

Procedure

Fill the hemisphere with rice. Carefully pour the contents of the hemisphere into the cone. What fraction of the cylinder does the hemisphere appear to fill?

Procedure

If the radius of the cone is r and the height is 2r, then what is the volume of the cone in terms of r? What is the formula for the volume of a sphere? The volume of a sphere with radius r is given by the formula: V=4/3πr 3