Volumes of Pyramids & Cones

1. Volumes of Pyramids & Cones Jazzlyn Sturgis

2. Volume of a Pyramid • V=1/3Bh • To find the Value of a Pyramid you multiply 1/3 by the area of the Base by the Height of the pyramid.

3. Note that the height and base of the Pyramid is as shown…

4. Sample Problems • Find the volume of a pyramid with a height of 5 in. and a base with a side measurement of 9 in. 2. Find the volume of this pyramid.

5. Answers • V=1/3Bh • V=1/3x18x5 • V=30in^3 • V=1/3x121x11 • V=443.7cm^3

6. Oblique Pyramid • Finding the volume for an Oblique Pyramid requires the same formula as a regular pyramid. However, the height of an Oblique Pyramid is the length of the perpendicular segment from the vertex to the plane of the base.

7. Sample • Find the volume of this Oblique Pyramid.

8. Answer • V=1/3Bh • V=1/3x49x7.5 • V=122.5in^3

9. Using the Pythagorean Theorem • Sometimes in order to find the height of a pyramid you will need to use the Pythagorean theorem (a2+b2=c2). • For example…

11. Volume of a Cone

12. Oblique Cone

13. SAMPLE 1. 2.

14. Answers • 1. V=1/3Bh • V=1/3x113.1x12 (area of the circle or base is pi times the radius squared which is pi times 36 which equals 113.1) • V=452.4m^3 • 2. V=1/3x1385.4x42 • V=19396.2mm^3