Math 10C
Measurement Lesson #5
Volume of Pyramids and Cones
Objective: By the end of this lesson you will be able to:
- Describe the relationship between the volumes of:
o pyramids and prisms with the same base and height
o cones and cylinders with the same base and height
- Determine the volume of a prism, pyramid, cylinder, or cone, using a physical object or
its labeled diagram
- Determine an unknown dimension of a pyramid, cylinder, or cone, given its volume and
remaining dimensions
We have seen that:

The volume of a pyramid is ________ that of a prism with the same base and height.

The volume of a cone is _______ that of a cylinder with the same base and height.
Volume of a Right Rectangular Prism and a Right Rectangular Pyramid
Volume of a Right Cylinder and a Right Cone
e.g. 1) Determine the volume of the rectangular pyramid shown.
Math 10C
Measurement Lesson #5
e.g. 2) A pile of gravel is shaped like a cone. It has a diameter of 4 yd and a height of 1.5 yd.
a) What is the volume of gravel in the pile to the nearest hundredth?
b) Gravel is often sold in cubic yards. If one cubic yard sells for $32, determine the
value of the gravel in the pile.
e.g. 3) A cone has a height of 4 m and a volume of 205 m3.
a) Determine the radius of the cone to the nearest metre.
b) Determine the surface area of the cone to the nearest square metre.
Assignment:
p. 42-43 #8-9, 12, 14-15, 18