12.6 – Surface Area and Volume of Spheres LAST NOTES OF THE YEAR! SPHERE NOT!
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Transcript of 12.6 – Surface Area and Volume of Spheres LAST NOTES OF THE YEAR! SPHERE NOT!
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12.6 – Surface Area and Volume of Spheres
LAST NOTES OF THE YEAR!
SPHERE NOT!
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Sphere: The set of all points in space equidistant from a given point
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Radius: Length from the center of the sphere to all the sides of the sphere
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Hemisphere: Half a sphere
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Great Circle: Plane that contains the center of the sphere, the radius is the same as the one for the sphere
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Surface Area of a Sphere:
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Surface Area of a Sphere:
24SA rπ=
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Volume of a Sphere:
343
V rπ=
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Find the surface area.24SA rπ=
24 (6)SA π=
2144SA cmπ= SA =4π(36)
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Find the surface area.24SA rπ=
24 (11)SA π=
2484SA inπ=11 11 SA =4π(121)
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Find the volume.34
3V rπ=
34 (5)3
V π=
V ≈166.67πm 3
4 (125)3
V π=
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Find the volume.34
3V rπ=
34 (10.5)3
V π=
31543.5V ydπ=
4 (1157.625)3
V π=
10.5 10.5
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The center of the sphere is C and its circumference is 17π feet.
a. What is half of the sphere called?
Hemisphere
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The center of the sphere is C and its circumference is 17π feet.
b. Find the radius of the sphere.
2C rπ=17 2 rπ π=
8.5 ft r=
2π 2π
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The center of the sphere is C and its circumference is 17π feet.
c. Find the diameter of the sphere.
r = 8.5ft
d = 17ft
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The center of the sphere is C and its circumference is 17π feet.
d. Find the volume of the hemisphere.
343
V rπ=
€
V = 43
π (8.5)3
€
V = 43
π (614.125)
V ≈818.83π ft3
V ≈409.42π ft3
€
12
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SA = 324π ft2
Find the radius of a sphere with the given information.
24SA rπ=2324 4 rπ π=
281 r=
9 ft r=
4π 4π
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Find the radius of a sphere with the given information.
V = 36π in3
343
V rπ=
34363
rπ π=34
34
327 rπ π= 327 r=3in r=
π π
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Find the radius of a sphere with the given information.
V = 2304π yd3
343
V rπ=
3423043
rπ π=34
34
31728 rπ π=31728 r=
12yd r=