Cones and Pyramids
Solid
Cone
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Definition and Volume Formula
A cone is a solid having a circular base
and a single vertex. If the vertex is
over the center of the base, it is called
a right cone. If it is not, it is called an
oblique cone.
V 
1
Bh
3
where B is the area of the base and h is
the height of the cone
Pyramid
A polyhedron with a polygonal base
and sides (faces) that meets at a single
point called the apex. The triangular
sides are called the lateral faces.
V 
Slant height
1
Bh
3
where B is the area of the base and h is
the height of the cone
The distance measured along a lateral
face from the base to the vertex of a
pyramid or cone is the slant height.
In the case of a pyramid, the slant
height is the height of the triangular
lateral face.
Sphere
The set of all points in 3-dimensional
space located a distance r (the radius)
from the center.
V 
4 3
r
3
where r is the length of the radius
Density
A measure of how much matter is in a
certain volume. Weight (mass) per
unit of volume.
denisty 
mass
volume
Example 1. Find the exact volume of the following solids below.
Diagram
Homework
1. Find the volume of the cone in terms of 𝜋.
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Note: the cone is an oblique cone
2. The slant height of a cone is 26 and the radius of the base is 10. Find the volume of the cone to the nearest
tenth.
3. Find the volume of pyramid below.
4. Find the volume of the sphere in terms of 𝜋. The diameter of the sphere is 12cm.
5. An ice cream cone is 11cm deep and 5cm across the opening of the cone. Two hemisphere-shaped scoops
of ice cream, which have a diameter of 5cm are placed on top of a cone. If the ice cream were to melt into
the cone, will it over flow.
2-dimensional representation
of the ice cream cone