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Solid Figures 6 th Grade Georgia Performance Standards: M6M3 Students will determine the volume of fundamental solid figures (right rectangular prisms, cylinders, pyramids, and cones). M6M4 Students will determine the surface area of solid figures (right rectangular prisms and cylinders). Gail Sherman 2010

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Volume CRCT Formula Sheet gives the following formula for the volume of all right solid figures: V = Bh Big B stands for the area of the base. Small b stands for the base of a plane figure, like a triangle. Very confusing. Huh? What? Pardon Me?

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Volume of a Rectangular Prism What is the shape of the BIG B base? rectangle Find the area of B. 3x10 = 30 What is the height? 5 Final Answer? 3x10x5 = 150 units³ 3 10 5

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Volume of a Cylinder What is the shape of B? circle Find the area of B. π x 4² = 16 What is the height? 9 Final answer? π x 4² x 9 = 144 π 9 4

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Volume of a Cone This cone & cylinder have the same size bases and they are the same height. Do they both hold the same amount of water? Which one holds more? How much more? Let’s experiment…

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Volume of a Cone You know that cylinder volume = Bh. You know a cone is 1/3 the volume of a cylinder. So…Volume of a cone is:

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Volume of a Cone Find the volume of the cone. Radius is 5. Height is 4

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Nets Draw a net of a cube. How many faces?

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Surface Area of a Cube Let’s name the faces of our cube. Front Back Top Bottom Left Right If each side is 3 inches long, find the surface area.

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Add the areas of the 6 faces! Front is…… 3x3=9 Back is……. 3x3=9 Top is……… 3x3=9 Bottom is… 3x3=9 Left is……… 3x3=9 Right is……. 3x3=9 And the TOTAL is 54 in²

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Rectangular Prism Just a box. Draw a net for this rectangular prism. 4 2 7

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How does your net compare? ☺ It’s ok to be different! ☺ Now find the surface area. 4 2 7

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.. Surface Area of a Rectangular Prism Front = Back = Top = Bottom = Right = Left = Total =

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Rectangular Prism Front = 4x7=28 Back = 4x7=28 Top = 2x7=14 Bottom = 2x7=14 Right = 2x4=8 Left = 2x4=8 Total = 100 units ²

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Do You See Any Shortcuts? S.A. =2(lw+lh+wh) S.A. = 2wl+2hl+2wh

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Cylinders Draw a net of a soup can.

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Net of a Cylinder ☺ It’s ok to be different! ☺

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Find Surface area If the soup can is 10 inches tall and has a radius of 3 inches. 10 3

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Hints… Look back at your net 2 circles What’s that formula again? 1 rectangle I know the height What is the width? Add the parts together

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Voila! π r² gives me area of a circle. 3.14 x 3 x 3 = I have 2 of them, so I’ll multiply that by 2 = 2 π r gives me circumference (width of rectangle) 2 x 3.14 x 3 x 10 = 188.4 Top = 28.26 Bottom = 28.26 Rectangle = 188.4 TOTAL = 244.92 in²

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Answering With Pi Sometimes there is no need to compute pi, because they want the answer to be precise and contain pi. In that case: π r² = π x 3² = 9 π 2 π r = 2 x π x 3 x 10 = 60 π 9 π + 9 π + 60 π = 78 π

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