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Volume of solids
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Sphere When you have to find half a sphere divide by 2
Example: Find the radius of a sphere with a volume of 72 meters cubed. π£= 4 3 βΞ β π 3 3β72π 3 = 4 3 βΞ β π 3 β3 216π 3 =3βΞ β π 3 216π 4Ξ 3 = 4Ξ 4Ξ π 3 54Ξ = π Ξ = 3 π 3
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Cylinder π= π«β π π βπ π= π«β (ππππππ) π βππ ππππ
Example: Find the volume of a cylinder that has a diameter of 20 inches and a height of two feet. The radius is 10 inches. Two feet equal 24 inches. π= π«β π π βπ π= π«β (ππππππ) π βππ ππππ π= π«β πππππππ π βππ ππππ π=ππππΞ ππππ π
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Cube π½=π π π½=π π πππ.πππ ππ π =π π 3 πππ.πππ ππ π = 3 π 3 9.5cm = a
Example: A cube has a volume of cm3ΒΒΒΒ. Find its height. π½=π π πππ.πππ ππ π =π π 3 πππ.πππ ππ π = 3 π 3 9.5cm = a
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Rectangular prism V= w*l*h
Example: What is the volume of the prism? V= 10m * 4m * 5m V = 200 m3
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Triangular Prism π½= πβπ π βπ―
Example: Find the volume of the triangular prism: π½=ππππ ππππππππβππ π½= πβπ π βππ π½=πππ
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Cone Example: Find the volume of the cone. Find the height
π π + π π = π π 5 2 + π 2 = 15 2 β β5 2 π 2 =200 π=10 2 =14.1 V= π π βπ«β π π β14.1 V= πππ.π
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Square Base Pyramid π= π π ππππ ππππππ βπππ π= π π πππβπππ βππ.πππ
Example: Find the volume of the pyramid. Find the height π π + π π = π π 6 2 + π 2 = 12 2 β β6 2 π 2 =108 π=6 3 =10.4cm π= π π πππβπππ βππ.πππ π=πππ.πππ3 π= π π ππππ ππππππ βπππ
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Rectangular Pyramid V= π π ππππ πππππππππ βπππ V= π π πππβππππ βπππ
Example: Find the volume of the pyramid. V= π π ππππ πππππππππ βπππ V= π π πππβππππ βπππ V= 80 cm3
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Triangular Base Pyramid
Example: Find the volume of the pyramid. V= π π ππππ ππππππππ βππππ V= π π πβπ π βππππ V= 96 ππ3
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