Section 12-6 Surface Areas and Volumes of Spheres
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Section 12-6Surface Areas and Volumes of Spheres
Essential Questions
How do you find surface areas of spheres?
How do you find volumes of spheres?
Vocabulary
1. Great Circle:
2. Pole:
3. Hemisphere:
Vocabulary
1. Great Circle:
2. Pole:
3. Hemisphere:
A circle formed when a plane intersects a sphere and the circle has the same center as the sphere
Vocabulary
1. Great Circle:
2. Pole:
3. Hemisphere:
A circle formed when a plane intersects a sphere and the circle has the same center as the sphere
The endpoints of the diameter of a great circle
Vocabulary
1. Great Circle:
2. Pole:
3. Hemisphere:
A circle formed when a plane intersects a sphere and the circle has the same center as the sphere
The endpoints of the diameter of a great circle
One of the two congruent halves of a sphere created by a great circle
Formulas
Surface Area of a Sphere:
Volume of a Sphere:
Formulas
Surface Area of a Sphere: SA = 4π r2
Volume of a Sphere:
Formulas
Surface Area of a Sphere: SA = 4π r2
Volume of a Sphere: V = 43π r3
Example 1Find the surface area of the sphere.
Example 1Find the surface area of the sphere.
SA = 4π r2
Example 1Find the surface area of the sphere.
SA = 4π r2
SA = 4π (4.5)2
Example 1Find the surface area of the sphere.
SA = 4π r2
SA = 4π (4.5)2
SA ≈ 254.47 in2
Example 2Find the surface area of a hemisphere with a diameter of 8 mm to the nearest hundredth.
Example 2Find the surface area of a hemisphere with a diameter of 8 mm to the nearest hundredth.
SA = 12 i4π r
2 + π r2
Example 2Find the surface area of a hemisphere with a diameter of 8 mm to the nearest hundredth.
SA = 12 i4π r
2 + π r2 r = 12 d
Example 2Find the surface area of a hemisphere with a diameter of 8 mm to the nearest hundredth.
SA = 12 i4π r
2 + π r2 r = 12 d
r = 12 (8)
Example 2Find the surface area of a hemisphere with a diameter of 8 mm to the nearest hundredth.
SA = 12 i4π r
2 + π r2 r = 12 d
r = 12 (8)
r = 4 mm
Example 2Find the surface area of a hemisphere with a diameter of 8 mm to the nearest hundredth.
SA = 12 i4π r
2 + π r2 r = 12 d
r = 12 (8)
r = 4 mm
SA = 2π (4)2 + π (4)2
Example 2Find the surface area of a hemisphere with a diameter of 8 mm to the nearest hundredth.
SA = 12 i4π r
2 + π r2 r = 12 d
r = 12 (8)
r = 4 mm
SA = 2π (4)2 + π (4)2
SA ≈150.8 mm2
Example 3Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
Example 3Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
SA = 4π r2
Example 3Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
SA = 4π r2 C = 2π r
Example 3Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
SA = 4π r2 C = 2π r14π = 2π r
Example 3Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
SA = 4π r2 C = 2π r14π = 2π r2π 2π
Example 3Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
SA = 4π r2 C = 2π r14π = 2π r2π 2πr = 7 in.
Example 3Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
SA = 4π r2 C = 2π r14π = 2π r2π 2πr = 7 in.
SA = 4π (7)2
Example 3Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
SA = 4π r2 C = 2π r14π = 2π r2π 2πr = 7 in.
SA = 4π (7)2
SA ≈ 615.75 in2
Example 4Find the volume of the sphere rounded to the
nearest hundredth.
Example 4Find the volume of the sphere rounded to the
nearest hundredth.
V = 43π r3
Example 4Find the volume of the sphere rounded to the
nearest hundredth.
V = 43π r3
V = 43π (4.5)3
Example 4Find the volume of the sphere rounded to the
nearest hundredth.
V = 43π r3
V = 43π (4.5)3
V ≈ 381.70 in3
Example 5Find the volume of a hemisphere with a diameter
of 6 feet to the nearest hundredth.
Example 5Find the volume of a hemisphere with a diameter
of 6 feet to the nearest hundredth.
V = 12i43π r3
Example 5Find the volume of a hemisphere with a diameter
of 6 feet to the nearest hundredth.
V = 12i43π r3 r = 1
2 d
Example 5Find the volume of a hemisphere with a diameter
of 6 feet to the nearest hundredth.
V = 12i43π r3 r = 1
2 d
r = 12 (6)
Example 5Find the volume of a hemisphere with a diameter
of 6 feet to the nearest hundredth.
V = 12i43π r3 r = 1
2 d
r = 12 (6)
r = 3 ft
Example 5Find the volume of a hemisphere with a diameter
of 6 feet to the nearest hundredth.
V = 12i43π r3 r = 1
2 d
r = 12 (6)
r = 3 ftV = 23π (3)3
Example 5Find the volume of a hemisphere with a diameter
of 6 feet to the nearest hundredth.
V = 12i43π r3 r = 1
2 d
r = 12 (6)
r = 3 ftV = 23π (3)3
V ≈ 56.55 ft3
Example 6Find the volume of a sphere that has a great
circle with an area of 9π square feet.
Example 6Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V = 43π r3
Example 6Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V = 43π r3 A = π r2
Example 6Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V = 43π r3 A = π r2
9π = π r2
Example 6Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V = 43π r3 A = π r2
9π = π r2π π
Example 6Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V = 43π r3 A = π r2
9π = π r2π π
9 = r2
Example 6Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V = 43π r3 A = π r2
9π = π r2π π
r = 3 ft.9 = r2
Example 6Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V = 43π r3 A = π r2
9π = π r2π π
r = 3 ft.9 = r2
V = 43π (3)3
Example 6Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V = 43π r3 A = π r2
9π = π r2π π
r = 3 ft.9 = r2
V = 43π (3)3
V ≈113.10 ft3
Problem Set
Problem Set
p. 868 #1-25 odd
“With self-discipline most anything is possible.” - Theodore Roosevelt
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