Volume of solids

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. 𝑣= 4 3 ∗Π∗ 𝑟 3 3∗72𝑚 3 = 4 3 ∗Π∗ 𝑟 3 ∗3 216𝑚 3 =3∗Π∗ 𝑟 3 216𝑚 4Π 3 = 4Π 4Π 𝑟 3 54Π= 𝑟 3 3 54Π = 3 𝑟 3

Cylinder 𝒗= 𝜫∗ 𝒓 𝟐 ∗𝒉 𝒗= 𝜫∗ (𝟏𝟎𝒊𝒏𝒄𝒉) 𝟐 ∗𝟐𝟒 𝒊𝒏𝒄𝒉 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. 𝒗= 𝜫∗ 𝒓 𝟐 ∗𝒉 𝒗= 𝜫∗ (𝟏𝟎𝒊𝒏𝒄𝒉) 𝟐 ∗𝟐𝟒 𝒊𝒏𝒄𝒉 𝒗= 𝜫∗ 𝟏𝟎𝟎𝒊𝒏𝒄𝒉 𝟐 ∗𝟐𝟒 𝒊𝒏𝒄𝒉 𝒗=𝟐𝟒𝟎𝟎Π𝒊𝒏𝒄𝒉 𝟐

Cube 𝑽=𝒂 𝟑 𝑽=𝒂 𝟑 𝟖𝟓𝟕.𝟑𝟏𝟓 𝒄𝒎 𝟑 =𝒂 𝟑 3 𝟖𝟓𝟕.𝟑𝟏𝟓 𝒄𝒎 𝟑 = 3 𝑎 3 9.5cm = a Example: A cube has a volume of 857.375 cm3­­­­. Find its height. 𝑽=𝒂 𝟑 𝟖𝟓𝟕.𝟑𝟏𝟓 𝒄𝒎 𝟑 =𝒂 𝟑 3 𝟖𝟓𝟕.𝟑𝟏𝟓 𝒄𝒎 𝟑 = 3 𝑎 3 9.5cm = a

Rectangular prism V= w*l*h Example: What is the volume of the prism? V= 10m * 4m * 5m V = 200 m3

Triangular Prism 𝑽= 𝒃∗𝒉 𝟐 ∗𝑯 Example: Find the volume of the triangular prism: 𝑽=𝒂𝒓𝒆𝒂 𝒕𝒓𝒊𝒂𝒏𝒈𝒍𝒆∗𝟏𝟐 𝑽= 𝟔∗𝟖 𝟐 ∗𝟏𝟐 𝑽=𝟐𝟖𝟖

Cone Example: Find the volume of the cone. Find the height 𝒂 𝟐 + 𝒃 𝟐 = 𝒄 𝟐 5 2 + 𝑏 2 = 15 2 −5 2 −5 2 𝑏 2 =200 𝑏=10 2 =14.1 V= 𝟏 𝟑 ∗𝜫∗ 𝟓 𝟐 ∗14.1 V= 𝟑𝟔𝟗.𝟏

Square Base Pyramid 𝒗= 𝟏 𝟑 𝒂𝒓𝒆𝒂 𝒔𝒒𝒖𝒂𝒓𝒆 ∗𝟔𝒄𝒎 𝒗= 𝟏 𝟑 𝟔𝒄𝒎∗𝟔𝒄𝒎 ∗𝟏𝟎.𝟒𝒄𝒎 Example: Find the volume of the pyramid. Find the height 𝒂 𝟐 + 𝒃 𝟐 = 𝒄 𝟐 6 2 + 𝑏 2 = 12 2 −6 2 −6 2 𝑏 2 =108 𝑏=6 3 =10.4cm 𝒗= 𝟏 𝟑 𝟔𝒄𝒎∗𝟔𝒄𝒎 ∗𝟏𝟎.𝟒𝒄𝒎 𝒗=𝟏𝟐𝟒.𝟖𝒄𝒎3 𝒗= 𝟏 𝟑 𝒂𝒓𝒆𝒂 𝒔𝒒𝒖𝒂𝒓𝒆 ∗𝟔𝒄𝒎

Rectangular Pyramid V= 𝟏 𝟑 𝒂𝒓𝒆𝒂 𝒓𝒆𝒄𝒕𝒂𝒏𝒈𝒍𝒆 ∗𝟔𝒄𝒎 V= 𝟏 𝟑 𝟒𝒄𝒎∗𝟏𝟎𝒄𝒎 ∗𝟔𝒄𝒎 Example: Find the volume of the pyramid. V= 𝟏 𝟑 𝒂𝒓𝒆𝒂 𝒓𝒆𝒄𝒕𝒂𝒏𝒈𝒍𝒆 ∗𝟔𝒄𝒎 V= 𝟏 𝟑 𝟒𝒄𝒎∗𝟏𝟎𝒄𝒎 ∗𝟔𝒄𝒎 V= 80 cm3

Triangular Base Pyramid Example: Find the volume of the pyramid. V= 𝟏 𝟑 𝒂𝒓𝒆𝒂 𝒕𝒓𝒊𝒂𝒏𝒈𝒍𝒆 ∗𝟏𝟐𝒄𝒎 V= 𝟏 𝟑 𝟔∗𝟖 𝟐 ∗𝟏𝟐𝒄𝒎 V= 96 𝒄𝒎3