Download Volume of Cones

Name ______________________________
Volume of Cones
Module 3
Learning Target: I can use the volume formula for a cone.
Opening Exercise
The altitude or height of a cone is a perpendicular segment from the vertex of the cone to the plane
of the base as shown in the diagram.
Determine the height of the right circular cone shown below.
Volume of Cones
Cones are three-dimensional closed figures. The vertex of a cone is the point opposite the base. The
axis of a cone is the segment with endpoints at the vertex and the center of the base. The axis of a
right circular cone is perpendicular to the base. The axis of an oblique cone is not perpendicular to
the base. The slant height of a right cone is the distance from the vertex of a right cone to a point on
the edge of the base. The altitude of a cone is a perpendicular segment from the vertex of the cone
to the plane of the base.
1. Determine the volume of the cone in terms of 𝜋.
2. Find the volume, in terms of 𝜋, of a cone with radius 7 cm and height 15 cm.
3. Determine the volume of the cone shown below. Give an exact answer.
4. Find the volume of the right circular cone, in cubic feet, to the nearest tenth.
5. A cone fits inside a cylinder so that their bases are the same and their heights are the same, as
shown in the diagram below. Calculate the volume that is inside the cylinder but outside of the cone.
Give an exact answer.
Name ______________________________
Volume of Cones
Module 3
Problem Set
𝟏
Volume: V= 𝟑 𝑩𝒉, where B is the area of the base
1. In the diagram below, a right circular cone has a diameter of 8 inches and a height of 12 inches.
What is the volume of the cone to the nearest cubic inch?
2. Determine the volume of the right circular cone below.
3. 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?
4. Find the volume of the funnel shown below.
5. Find the difference in the volumes of the cones created by rotating the triangle shown below
around the x-axis and around the yaxis. Write your answer in terms of 𝜋.
6. An hourglass, composed of two cones, is 12 cm tall. The radius of each cone is 3 cm. If you want to
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fill the bottom half of the hourglass 3 full of salt, how much salt will you need?
7. Students in one mathematics class noticed that a local movie theater sold popcorn in different
shapes of containers, for different prices. They wondered which of the choices was the best buy.
Analyze the three popcorn containers below. Which is the best buy? Explain.
Name ______________________________
Volume of Cones
Module 3
Exit Ticket
The right circular cone shown has a base with radius of 7. The slant height of the cone’s lateral
surface is √130. Find the volume of the cone.