Name: __________________________
11.5 & 11.6 Volume of Prisms, Cylinder, Pyramid
Date: __________
Volume – the number of cubic units needed to fill a solid.
To find the volume of a prism or cylinder, multiply the base area (B) by the height h.
Rectangular Prisms
Formula:
___________________
Example 1:
B= ____________
B = _________
h =____________
h =___________
V= _______________
V= ____________
Find the volume of each prism.
a)
b)
c)
Cylinders – have two bases that are parallel, congruent circles. Formula: _________________________
Example 2:
B = ___________
B = ___________
h = ____________
h = ____________
V = ___________
V = ___________
1
Try on your own:
Pyramid – has a base shape meeting at a common vertex. Formula: __________
Find the volume of the pyramid.
B= ____________
h = ____________
V= ____________
Find the volume of the pyramid.
Find the height of the triangular pyramid.
2
Similar Solids
Two solids of the same type with equal ratios of corresponding linear measures, such as heights or radii, are
called similar solids. The ratio of the corresponding linear measures of two similar solids is called the scale
factor. If two similar solids have a scale factor of k, then the ratio of their volumes is equal to k3.
Example: Finding the Volume of a Similar Solid
1) Cylinder A and cylinder B are similar.
Find the volume of cylinder B.
2)
Finding the Volume of a Composite Solid
Find the volume of the concrete block.
3
Using the Formula for Density
Density is the amount of matter that an object has in a given unit of volume.
𝑫𝒆𝒏𝒔𝒊𝒕𝒚 =
𝑴𝒂𝒔𝒔
𝑽𝒐𝒍𝒖𝒎𝒆
Example:
The diagram shows the dimensions of a standard gold bar at Fort Knox. Gold
has a density of 19.3 grams per cubic centimeter. Find the mass of a standard
gold bar to the nearest gram.
Modeling
You are building a rectangular chest. You want the length to be 6 feet, the width
to be 4 feet, and the volume to be 72 cubic feet. What should the height be?
Solving a Real-Life Problem
You are building a 6-foot-tall dresser. You want the volume to be 36 cubic feet. What should
the area of the base be? Give a possible length and width.
4
Find the volume of Q1 and 2.
3. A pyramid with a rectangular base has a volume of 60 cubic feet and a height of 6 feet. The width of the
rectangular base is 4 feet. Find the length of the rectangular base.
4. A pyramid with a triangular base has a volume of 80 cubic meters and a base area of 20 square meters.
Find the height of the pyramid.
5. Find the volume of the cylinder with a radius of 5 ft and height of 4 ft.
6. Find the volume of the composite solid.
7. Find the missing dimension
8. The prisms are similar. Find the volume of Prism B.
9.
5
A cylindrical container with a radius of 12
centimeters is filled to a height of 6 centimeters
with coconut oil. The density of coconut oil is 0.92
gram per cubic centimeter. What is the mass of the
coconut oil to the nearest gram?