# 2. - Omni Middle School

```Quiz
Find the volume of each figure to the nearest
tenth.Use 3.14 for p.
1. the triangular pyramid
2. the cone
Find the surface area of each figure to the nearest
tenth. Use 3.14 for p.
3. the triangular prism
4. the cylinder
Surface and Area of
Pyramids
and Cones
6.9
Pre-Algebra
Warm Up
1. A rectangular prism is 0.6 m by 0.4 m by 1.0 m.
What is the surface area?
2.48 m2
2. A cylindrical can has a diameter of 14 cm and a
height of 20 cm. What is the surface area to the
nearest tenth? Use 3.14 for p.
1186.9 cm2
Learn to find the surface area of pyramids
and cones.
Vocabulary
slant height
regular pyramid
right cone
The slant height of a
pyramid or cone is measured
along its lateral surface. Right cone
Regular
Pyramid
The base of a regular
pyramid is a regular
polygon, and the lateral
faces are all congruent.
In a right cone, a line perpendicular to the
base through the tip of the cone passes through
the center of the base.
Example: Finding Surface Area
Find the surface area of each figure
1
Pl
2
1
= (2.4 • 2.4) +
(9.6)(3)
2
= 20.16 ft2
A. S = B +
B. S = pr2 + prl
= p(32) + p(3)(6)
= 27p  84.8 cm2
Try This
Find the surface area of each figure.
1
Pl
2
1
= (3 • 3) +
(12)(5)
2
= 39 m2
5m
A. S = B +
3m
3m
B. S = pr2 + prl
=
p(72)
+ p(7)(18)
= 175p  549.5
ft2
18 ft
7 ft
Example: Exploring the Effects of
Changing Dimensions
A cone has diameter 8 in. and slant height 3
in. Explain whether tripling the slant height
would have the same effect on the surface
area as tripling the radius.
They would not have the same effect. Tripling the
radius would increase the surface area more than
tripling the slant height.
Try This
A cone has diameter 9 in. and a slant height
2 in. Explain whether tripling the slant
height would have the same effect on the
surface area as tripling the radius.
Original Dimensions
S = pr2 + pr(3l)
S = pr2 + prl
= p(4.5)2 + p(4.5)(2)
= 29.25p in2
Triple the Slant
Height
 91.8 in2
= p(4.5)2 + p(4.5)(6)
= 47.25p in2
 148.4 in2
S = p(3r)2 + p(3r)l
= p(13.5)2 + p(13.5)(2)
= 209.25p in2
 657.0 in2
They would not have the same effect. Tripling the
radius would increase the surface area more than
tripling the height.
Example: Application
The upper portion of an hourglass is
approximately an inverted cone with the given
dimensions. What is the lateral surface area of
the upper portion of the hourglass?
a2 + b2 = l2
102 + 262 = l2
l  27.9
L = prl
Pythagorean Theorem
Lateral surface area
= p(10)(27.9)  876.1 mm2
Try This
A road construction cone is almost a full cone.
With the given dimensions, what is the lateral
surface area of the cone?
a2 + b2 = l2
Pythagorean Theorem
42 + 122 = l2
l  12.65
L = prl Lateral surface area
= p(4)(12.65)  158.9 in2
12 in.
4 in.
Lesson Quiz: Part 1
Find the surface area of each figure to
the nearest tenth. Use 3.14 for p.
1. the triangular pyramid
6.2 m2
2. the cone
175.8 in2
Lesson Quiz: Part 2
3. Tell whether doubling the dimensions of
a cone will double the surface area.
It will more than double the surface area
because you square the radius to find the
area of the base.
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