Chapter 10 Surface Area and Volume

1
Chapter 10 Surface Area and Volume

• 10.3 Surface Area of Prisms and Cylinders
• 10.4 Surface Areas of Cones and Pyramids
• 10.5 Volume of Prisms and Cylinders
• 10.6 Volume of Cones and Pyramids
• 10.7 Surface Area and Volume of Spheres

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Surface Areas of Prisms and Cylinders

• Surface Area Area of all of the sides added
  together
• Prism Polyhedron with exactly two congruent,
  parallel faces, called bases
• Lateral faces Other faces, not the bases

3
Surface Area of Prisms

• Lateral Area is the sum of the areas of the
  lateral faces
• Surface Area is the sum of the lateral area and
  the area of the two bases

4
Surface Area of Prisms

• Lateral Area ph
• p perimeter of the base
• h height of the prism
• Surface Area ph 2B
• p perimeter of the base
• h height of the prism
• B area of the base

5
Surface Area of a Prism

• Find the surface area and lateral area of the
  prism.

S.A. ph 2B
S.A. (14)(5) 2(12)
S.A. 70 24
5cm
S.A. 94cm2
What is the lateral Area?
3cm
L.A. 70cm2
4cm
Do examples from book
6
Surface Area of a Cylinder

• Lateral Area 2prh
• r radius
• h height of the cylinder
• Surface Area 2prh 2pr2
• r radius
• h height

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Surface Area of a Cylinder

• Find the Surface Area of a Cylinder.

S.A. 2prh 2pr2
4in
S.A. 2p(4)(6) 2p(4)2
S.A. 48p 32p
S.A. 80p in2
6in
What is the lateral area?
L.A. 48p in2
Do examples from book
8
Volume of Prisms and Cylinders

• Volume Space that a figure occupies or the
  space inside a figure how much it can hold

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Volume of a Prism

• Volume V Bh
• B area of the base
• h height of prism

10
Volume of a Prism

• Find the Volume of the Prism

V Bh
V (24)(20)(10)
V 4800 cm3
10cm
20cm
24cm
Look at Examples in Book
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Volume of a Cylinder

• Volume V pr2h
• r radius
• h height of the cylinder

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Volume of a Cylinder

• Find the Volume of the Cylinder

V pr2h
V p(3)2(8)
3cm
V 72p cm3
8cm
Do examples from book
13
Surface Areas of Pyramids and Cones

• Pyramid Polyhedron in which one face (the base)
  can be any polygon and the other faces (the
  lateral faces) are triangles that meet at a
  common vertex.
• You name a pyramid by the shape of its base
  (triangular pyramid, rectangular pyramid, etc)

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Surface Areas of Pyramids and Cones

• The height of a pyramid is perpendicular to the
  base
• The slant height l is the height of one of the
  lateral faces
• Look in book, pg 537 at diagram

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Surface Area of a Pyramid

• Lateral Area ½pl
• p perimeter of the base
• l slant height (or lateral height)
• Surface Area ½pl B
• p perimeter of the base
• l slant height (or lateral height)
• B Area of the base

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Surface Area of a Pyramid

• Find the Surface Area of the Pyramid

S.A. ½pl B
S.A. ½(48)(11) (144)
11in
S.A. 264 144
S.A. 408in2
What is the lateral area?
12in
L.A. 264in2
Do examples in book
17
Surface Area of Cones

• Cone pointed like a pyramid, but its base is
  a circle
• The height is a segment from the vertex that is
  perpendicular to the base
• The slant height is the height of the side of
  the cone
• Look at picture on page 539

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Surface Area of a Cone

• Lateral Area prl
• r radius
• l lateral height
• Surface Area prl pr2
• r radius
• l lateral height

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Surface Area of a Cone

• Find the Surface Area of the cone

S.A. prl pr2
S.A. p(15)(25) p(15)2
S.A. 375p 225p
S.A. 600p cm2
25cm
What is the lateral area?
L.A. 375p cm2
15cm
Do examples from book
20
Volume of a Pyramid

• V 1/3 Bh
• B Area of the base
• h height of the pyramid

Notice that the formula for volume of a pyramid
is the same as the volume for a prism, except you
take times 1/3. This is because the pyramid is
1/3 the size of the prism if they have the same
base.
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Volume of a Pyramid

• Find the Volume of the Pyramid

V 1/3Bh
h 12ft
V 1/3(40)(40)(12)
V 6400ft3
40ft
Do examples from book
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Volume of a Cone

• V 1/3 pr2h
• r radius
• h height

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Volume of a Cone

• Find the volume of the cone

V 1/3 pr2h
V 1/3 p(15)2(25)
25ft
V 1875p ft3
15ft
Do examples from book
24
Surface Area and Volume of Spheres

• Sphere Set of all points in space equidistant
  from a given point called the center
• Radius Segment that has one endpoint at the
  center and the other endpoint on the sphere

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Surface Area of a Sphere

• Surface Area 4pr2

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Surface Area of a Sphere

• Find the surface area of the sphere

S.A. 4pr2
S.A. 4p(4)2
S.A. 64p cm2
Radius 4cm
Work on examples from book
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Volume of a Sphere

• V 4/3pr3

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Volume of a Sphere

• Find the volume of a sphere

V 4/3 pr3
V 4/3 p(3)3
V 36p ft3
Radius 3ft
Examples from book