5. a) Use the formula for surface area of a right pyramid with a regular polygon base and slant
height s:
Surface area =
s(perimeter of base) + (base area)
When the base is a square with side length l,
Surface area =
s(4l) + l2
Surface area =
(11)(4)(6) + (6)2
Substitute: s = 11, l = 6
Surface area = 132 + 36
Surface area = 168
The surface area of the square pyramid is 168 square inches.
b) Use the formula for surface area of a right pyramid with a regular polygon base and slant
height s:
Surface area =
s(perimeter of base) + (base area)
When the base is an equilateral triangle with side length l,
Surface area =
s(3l) +
s(l) Substitute: s = 11.3, l = 13.0
Surface area =
(11.3)(3)(13.0) +
(13)(11.3)
Surface area = 220.35 + 73.45
Surface area = 293.8
The surface area of the regular tetrahedron is approximately 294 cm2.
6. a) Use the formula for the lateral area, AL, of a right cone with base radius r and
slant height s.
AL =
Substitute: r = 4, s = 8
AL = π(4)(8)
AL = 100.5309…
The lateral area of the right cone is approximately 101 square inches.
7. a) Use the formula for the surface area of a right cone with base radius r and
slant height s.
Surface area =
+
Substitute: r = 4, s = 8
Surface area = π(4)(8) + π(4)2
Surface area = 150.7964…
The surface area of the right cone is approximately 151 square inches.
b) Use the formula for the surface area of a right cone with base radius r and
slant height s.
Surface area =
+
Substitute: r = 15, s = 35
Surface area = π(15)(35) + π(15)2
Surface area = 2356.1944…
The surface area of the right cone is approximately 2356 cm2.
11. Sketch the cone.
a) Use the formula for the lateral area, AL, of a right cone with base radius r and
slant height s:
AL =
Substitute: r = 16, s = 45
AL = π(16)(45)
AL = 2261.9467…
The lateral area of the volcano is approximately 2261.9 cm2.
b) To determine the number of jars needed, divide the total area by the area covered by one
jar:
5.7
Since Aiden cannot buy part of a jar of paint, 6 jars are needed.
The total cost is: 6($1.99), or $11.94
The paint will cost $11.94.
15. Sketch and label a diagram. Let s represent the slant height.
The radius of the cone is 6 ft.
Use the Pythagorean Theorem in right ∆ACD.
AD2 = AC2 + CD2
s2 = 82 + 62
s2 = 64 + 36
s2 = 100
s=
s = 10
Use the formula for the lateral area, AL, of a right cone with base radius r and slant height s:
AL =
Substitute: r = 6, s = 10
AL = (6)(10)
AL = 188.4955…
The surface area of the exposed grain is approximately 188 square feet.