A glass vase is in the shape of a cylinder with a cone shaped opening. The height of the cylinder is 33 cm and the diameter is 20 cm. How much glass is needed to make the vase?

1 Answer
Jun 11, 2017

The amount of glass required is 2200picm^32200πcm3 or 6908cm^36908cm3.

Explanation:

Presuming the height of the cone also to be 33cm33cm (the presumption being that the tip of the cone-shaped opening is at the other end of the cylinder), and that the diameter is the same for both, the method we use is to subtract the volume of the cone from the volume of the cylinder - that will give us the volume of glass required.

Hence:
Vg=Vcy-VcoVg=VcyVco

The formula for volume of a cylinder is:
Vcy=pir^2hVcy=πr2h, where r=r=radius, and h=h=height.

The formula for volume of a cone is:
Vco=pir^2h/3Vco=πr2h3

Hence:
Vg=Vcy-VcoVg=VcyVco

Vg=pir^2h-pir^2h/3Vg=πr2hπr2h3

Vg=pir^2h(1-1/3)Vg=πr2h(113)

Vg=pir^2h(2/3)Vg=πr2h(23)

Vg=pixx10^2xx33xx2/3Vg=π×102×33×23

Substitute 1010 for rr (radius is half the diameter), and 3333 for hh.

Vg=pixx100xx11cancel33xx2/(1cancel3)

Vg=pixx100xx11xx2

Vg=pixx2200

Vg=2200pi

Considering pi=3.14:

Vg=6908