Geometric Solids
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Geometric Solids
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Geometric Solids. Use the following key for the formulas in this presentation. b = based = diameter h = heightr = radius l = lengthpi = 3.14 w = width l = slant height. The cylinder has two circular bases. Cylinder. r. h. Volume = (pi)r 2 h. Cylinder. r. h. - PowerPoint PPT Presentation
Transcript of Geometric Solids
Geometric Solids
Use the following key for the formulas in this
presentation.
• b = base d = diameter• h = height r = radius• l = length pi = 3.14• w = width l = slant
height
Cylinder
• The cylinder has two circular bases. h
r
Cylinder
• Volume = (pi)r2hh
r
Cylinder
• SA = 2(pi)rh +2(pi)r2
h
r
Cone
• The cone consist of one circular base.
l h
r
Cone
• Volume = 1/3(pi)r2h l h
r
Cone
• SA = (pi)rl + (pi)r2 l h
r
Sphere
r
• V = (4/3)(pi)r3
Sphere
r• SA = 4(pi)r2
Rectangular Prism
• The Rectangular Prism has two rectangular bases.
w
h
l
Rectangular Prism
• V = lwh
w
h
l
Rectangular Prism
• SA = 2(lw + hw + lh)
w
h
l
Square Pyramid
• The Square Pryamid has one square base.
l
l
h
w
Square Pyramid
• V = (1/3)lwh l
l
h
w
Square Pyramid
• SA = 2ll + l2 l
l
h
w
Example Problems
Find the volume of the cylinder.
10 in
6 in
Find the volume of the cylinder.
• V = (pi) r2h
10 in
6 in
Find the volume of the cylinder.
• V = (pi) r2h• pi = 3.14• r = 6• h = 10 10 in
6 in
Find the volume of the cylinder.
• V = (pi) r2h• pi = 3.14• r = 6• h = 10• V = (3.14)(62)(10)
10 in
6 in
Find the volume of the cylinder.
• V = (pi) r2h• pi = 3.14• r = 6• h = 10• V = (3.14)(62)(10)• V = 1130.4 in3
10 in
6 in
Find the surface area of the sphere.
14 cm
Find the surface area of the sphere.
• SA = 4(pi)r2
14 cm
Find the surface area of the sphere.
• SA = 4(pi)r2
• pi = 3.14• diameter = 14 so…• r = 7
14 cm
Find the surface area of the sphere.
• SA = 4(pi)r2
• pi = 3.14• diameter = 14 so…• r = 7• SA = 4(3.14)(72)
14 cm
Find the surface area of the sphere.
• SA = 4(pi)r2
• pi = 3.14• diameter = 14 so…• r = 7• SA = 4(3.14)(72)• SA = 615.4 cm2
14 cm
Find the volume of the prism.
1 ft
4 in
8 in
Find the volume of the prism.
• V = lwh 1 ft
4 in
8 in
Find the volume of the prism.
• V = lwh• l = 8 in• w = 4 in• h = 1 ft = 12 in 1 ft
4 in
8 in
Find the volume of the prism.
• V = lwh• l = 8 in• w = 4 in• h = 1 ft = 12 in• V = (8)(4)(12)
1 ft
4 in
8 in
Find the volume of the prism.
• V = lwh• l = 8 in• w = 4 in• h = 1 ft = 12 in• V = (8)(4)(12)• V = 384 in3
1 ft
4 in
8 in
r=8 in
r= 1 ft
r= 1.8 ft
How much snow did it take to make the
snowman?
r=8 in
r= 1 ft
r= 1.8 ft
How much snow did it take to make the
snowman?• Volume of top:
(4/3)(3.14)(.73) = 1.4 ft3
r=8 in
r= 1 ft
r= 1.8 ft
How much snow did it take to make the
snowman?
• Volume of middle: (4/3)(3.14)(13) = 4.2 ft3
r=8 in
r= 1 ft
r= 1.8 ft
How much snow did it take to make the
snowman?
• Volume of bottom: (4/3)(3.14)(1.83) = 24.4 ft3
r=8 in
r= 1 ft
r= 1.8 ft
How much snow did it take to make the
snowman?
• Total Volume: • 1.4 + 4.2 + 24.4
= 30 ft3
