GEOMETRY
Lesson 4
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:_______________________________________
M3
Period:________ Date:_________
Lesson 4: Volumes of Pyramids and Cones
Learning Targets

I can calculate the volumes of pyramids.

I can apply the properties of right triangles and trigonometry to find the volume of pyramids
Volumes of pyramids
Definition: Volume is the space that a three-dimensional figure can occupy. Ex: The volume of a glass is the
amount of liquid it can hold.
The volume of a pyramid
Example 1. Find the volume of the
pyramid
V= (1/3) Area Base * height or
𝑉 = _____________
The volume of the cone
𝑽 = ____________________
http://youtu.be/0ZACAU4SGyM.
Example 2. Find the volume of the cone
GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:_______________________________________
Applications of Right Triangles and
Trigonometry
Lesson 4
M3
Period:________ Date:_________
Example 3. Find the volume of the cone when
the slant height is 12 and radius is 4
To calculate the volume of the right cone we
might be given slant height, height and the
radius and the angle formed between the
slant height and radius
Example 4. What is the volume of the cone?
Example 5 What if the volume of the
cone that is part of this water tower
If 𝐹𝐷 = 8.5 ft and
, determine
and state, to the nearest cubic foot, the volume of
the water tower.
GEOMETRY
Lesson 4
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:_______________________________________
M3
Period:________ Date:_________
Lesson 4: Volumes of Pyramids and Cones
Classwork
1. Find the volume of each pyramid
a.
b.
2. Find the volume of the cone in terms of  .
a.
b.
c.
3. The cone and the cylinder have the same base and the same height. If the cone is filled with liquid and
poured into the cylinder repeatedly, how many times would it take to fill the cylinder (explain your answer)
GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:_______________________________________
Lesson 4
M3
Period:________ Date:_________
Lesson 4: Volumes of Pyramids and Cones – Day 2
Composite Figures
1. Find the volume of the composite figure.
2. Many of the ancient pyramids of Egypt are still buried in the sand. Satellites can now locate some
of these buried structures using advanced technology. One of the buried pyramids has a height if
250 feet and square base with a side length of 340 feet. How much sand, to the nearest thousand
cubic feet, is displaced by the pyramid?
3. A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 12 cm, a
width of 6 cm, and a height of 8 cm. The pyramid has a height of 10 cm. Find the volume of the
composite figure.
4. A conical grain storage tank has a height of 30 meters and a diameter of 14 meters. Find the
capacity of the storage tank. Round the answer to the nearest square meter.
GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:_______________________________________
Lesson 4
M3
Period:________ Date:_________
5. The vertex of a right cone has a 20o angle and the slant height is 10 cm. Find the volume of the
cone.
6. Jessica and Michele are working on a science lab project where they are creating salt solutions.
Jessica’s container is in the shape of a rectangular prism which is 2 inches wide, 4 inches long and 8
inches high. She fills it with water up to the 6 inch mark and adds 15 grams of salt to the water.
Michele’s container is right triangular prism whose triangular base has legs that are 3 and 6 inches,
respectively. The height of her container is also 8 inches. She fills in with water to the 7 inch mark and
adds 15 grams of salt to the water. Which container has the greatest concentration of salt? Justify your
solution
7. Suppose you fill a conical paper cup with a height of 6" with water. If all the water is then poured
into a cylindrical cup with the same radius and same height as the conical paper cup, to what
height will the water reach in the cylindrical cup?
8. Sand falls from a conveyor belt and forms a pile on a flat surface. The diameter of the pile is
approximately 10 ft. and the height is approximately 6 ft. Estimate the volume of the pile of sand.
State your assumptions used in modeling.
GEOMETRY
Lesson 4
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:_______________________________________
Period:________ Date:_________
Lesson 4: Volumes of Pyramids and Cones – Day 2
Day 2 - Problem Set
1. Identify the solid shown, and find its volume.
2. Find the volume of the right rectangular pyramid shown.
3. Find the volume of the circular cone in the diagram. (Use
M3
22
7
as an approximation of pi.)
GEOMETRY
NYS COMMON CORE MATHEMATICS CURRICULUM
Name:_______________________________________
Lesson 4
M3
Period:________ Date:_________
4. Find the volume of the cone.
5. If a cone has height 9 ft and volume 75 ft3, find the radius of the base.
6. The vertex of a right cone has a 40o angle and the slant height is 12 cm. Find the volume of the cone.