Volume of Pyramids, Cones & Spheres

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Given the same diameter and height for each figure, drag them to arrange in order of smallest to largest volume.

How many filled cones do you think it would take to fill the cylinder?

How many filled spheres do you think it would take to fill the cylinder?

Demonstration comparing volume of Cones & Spheres with volume of Cylinders

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Volume of a Cone

(Area of Base x Height) 3

(Area of Base x Height) 1 3

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A cone is 1/3 the volume of a cylinder with the same base area (B) and height (h).

V = 2/3 (Volume of Cylinder)

r2 h)2/3 (V =

or

V = 4/3 r3

Volume of a Sphere

click to reveal

A sphere is 2/3 the volume of a cylinder with the same base area (B) and height (h).

How much ice cream can a Friendly’s Waffle cone hold if it has a diameter of 6 in and its height is 10 in?

(Just Ice Cream within Cone. Not on Top)

23 Find the volume.

4 in

9 in

24 Find the Volume

5 cm8 cm

If the radius of a sphere is 5.5 cm, what is its volume?

25 What is the volume of a sphere with a radius of 8 ft?

26 What is the volume of a sphere with a diameter of 4.25 in?

Volume of a Pyramid

(Area of Base x Height) 3

(Area of Base x Height) 1 3click to reveal

A pyramid is 1/3 the volume of a prism with the same base area (B) and height (h).

Pyramids are named by the shape of their base..

The volume is a pyramid is 1/3 the volume of a prism with the same base area(B) and height (h).

V = Bh13

=5 m

side length = 4 m

V = Bh13

27 Find the Volume of a triangular pyramid with base edges of 8 in, base height of 4 in and a pyramid height of 10 in.

8 in

10 in

4 in

28 Find the volume.

8 cm

7 cm

15.3 cm