Download Chapter 11 - Math at the Academy

Chapter 11
Surface Area and Volume
• Objectives:
1. Find the surface area of the following figures:
a)
b)
c)
d)
e)
Prisms
Cylinders
Pyramids
Cones
Spheres
2. Find the volume of the following figures:
a)
b)
c)
d)
e)
Prisms
Cylinders
Pyramids
Cones
Spheres
Prisms
• Prism: a polyhedron (3-dimensional figure whose faces are polygons)
with two congruent, parallel faces called ______________
• The other faces are _______________________________
• Name a prism using the ____________________________
• Prisms can be described as _____________ or _______________
Surface Area of a Prism
• Lateral Area: sum of the areas of the lateral faces
lateral area = ______________________________
• Surface Area: sum of the areas of the lateral faces and the areas of
the two bases
surface area = ____________________________
Objective 1(a)
• Find the surface area of each prism.
Cylinders
• Cylinder: a solid that has 2 congruent parallel bases that are
________________.
• Cylinders can be described as _____________ or _______________
Surface Area of a Cylinder
• Lateral area: the product of the circumference of the base and the
height of the cylinder
lateral area = _______________________
• Surface area: the sum of the lateral area and the areas of the two
bases
surface area = _______________________
Objective 1(b)
• Find the surface area of each cylinder.
Pyramids
• Pyramid: a polyhedron in which one face (the _________) can be any
polygon, and the other faces (the ________________) are triangles
that meet at a common vertex.
• Regular pyramid: base is a ________________________and lateral faces are
congruent __________________________
• Altitude (height): perpendicular segment from the vertex to the plane
of the base
• Slant height (l): the length of the altitude of a __________________
Surface Area of a Pyramid
• Lateral Area: half the product of the perimeter of the base and the
slant height
lateral area = ________________________
• Surface Area: the sum of the lateral area and the area of the base
surface area = ________________________
Objective 1(c)
• Find the surface area of each pyramid
Cones
• Cone: a solid that has one base that is a ____________ and a vertex
not in the same plane as the base
Surface Area of a Cone
• Lateral area: half the product of the circumference of the base and
the slant height of the cone
lateral area = _______________________________
• Surface area: the sum of the lateral area and the area of the base
surface area = ______________________________
Objective 1(d)
• Find the surface area of each cone.
Spheres
• Sphere: a set of all points in space _____________________from a
given point (center)
Surface Area of a Sphere
• Surface area: four times the product of π and the square of the radius
of the sphere
surface area = ______________________________
Objective 1(e)
• Find the surface area of the sphere
• Sphere with radius of 5 inches
• Sphere with diameter of 18 feet
Practice
• Find the surface area.
Practice
• Find the surface area.
Practice
• Find the surface area.
Volume of a Prism
• Volume of a prism: the product of the ___________________and the
______________of the prism
Volume = ______________________
Objective 2(a)
• Find the volume.
Volume of a Cylinder
• Volume of a cylinder: the product of the _________________and the
______________ of the cylinder
Volume = ______________________
Objective 2(b)
• Find the volume
Volume of a Pyramid
• Volume of a pyramid: _______________the product of the area of
the base and the height of the pyramid
Volume = ______________________
Objective 2(c)
• Find the volume.
Volume of a Cone
• Volume of a cone: one third the product of the area of the base and
the height of the cone
Volume = ______________________
Objective 2(d)
• Find the volume.
Volume of a Sphere
• Volume of a sphere: _____________the product of π and the cube of
the radius of the sphere
Volume = ______________________
Objective 2(e)
• Find the volume.
Practice
• Find the volume.
Practice
• Find the volume.