In order to answer his questions, Alonzo decided to get out his set of plastic geometry models. He has a sphere, cone, and cylinder that each has the same radius and height.

A. Draw an example diagram of each shape.

B. If the radius of the sphere is r, what is the height of the cylinder? How do you know?

C. Alonzo’s models are hollow and are designed to hold water. Alonzo was pouring water between the shapes, comparing their volumes. He discovered that when he poured the water in the cone and the sphere into the cylinder, the water filled up the cylinder without going over! Determine what the volume of the sphere must be if the radius of the sphere is r units. Show all work. Yes

Volume is defined as the space occupied by any object in the three-Dimenions. All three parameters are required for the volume like length, width and height of cube or cuboid.

Here for the part A If the radius of the sphere is r, what is the height of the cylinder the solution will be given as:-

The Volume of sphere = Volume of cylinder

4πr³=(π÷4) r²H

H=16r

H=4√r

Hence the height of the cylinder will be H=4√r

B. The volume of the shapes will be given as:-

(1) Volume of cylinder = (π÷4)r²H

Here r= radius of the cylinder

H = height of the cylinder

(2) The Volume of the Sphere=4πr³

Here r= radius of the cylinder

(3) The Volume of cone=(1÷3)πr³l

Here r = radius of the base

l=slant height of the cone

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