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Volume and Surface Area 7 th Grade More about Geometry Unit

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Definition Surface Area – is the total number of unit squares used to cover a 3-D surface.

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Find the SA of a Rectangular Solid Front Top Right Side A rectangular solid has 6 faces. They are: Top Bottom Front Back Right Side Left Side Which of the 6 sides are the same? Top and Bottom Front and Back Right Side and Left Side We can only see 3 faces at any one time.

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Surface Area of a Rectangular Solid Front Top Right Side We know that Each face is a rectangle. and the Formula for finding the area of a rectangle is: A = lw Steps: Find: Area of Top Area of Front Area of Right Side Find the sum of the areas Multiply the sum by 2. The answer you get is the surface area of the rectangular solid.

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Find the Surface Area of the following: 12 m 8 m 5 m Top Front Right Side Front Top Right Side Find the Area of each face: 12 m 5 m 12 m 8 m 5 m 8 m A = 12 m x 5 m = 60 m 2 A = 12 m x 8 m = 96 m 2 A = 8 m x 5 m = 40 m 2 Sum = 60 m 2 + 96 m 2 + 40 m 2 = 196 m 2 Multiply sum by 2 = 196 m 2 x 2 = 392 m 2 The surface area = 392 m 2

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Find the Surface Area 6 cm 4 cm 14 cm Area of Top = 6 cm x 4 cm = 24 cm 2 Area of Front = 14 cm x 6 cm = 84 cm 2 Area of Right Side = 14 cm x 4 cm = 56 cm 2 Find the sum of the areas: 24 cm 2 + 84 cm 2 + 56 cm 2 = 164 cm 2 Multiply the sum by 2: 164 cm 2 x 2 = 328 cm 2 The surface area of this rectangular solid is 328 cm 2. 24 m 2 84 m 2 56 m 2

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Nets A net is all the surfaces of a rectangular solid laid out flat. Top Right Side Front 10 cm 8 cm 5 cm Top Bottom Front Back Right SideLeft Side 10 cm 5 cm 8 cm 5 cm

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Top Right Side Front 10 cm 8 cm 5 cm Top Bottom Front Back Right SideLeft Side 10 cm 5 cm 8 cm 5 cm Find the Surface Area using nets. Each surface is a rectangle. A = lw Find the area of each surface. Which surfaces are the same? Find the Total Surface Area. 80 50 40 What is the Surface Area of the Rectangular solid? 340 cm 2

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Volumes Of Rectangular Prisms. Look at the rectangular prism below: 10cm 3cm 4cm We must first calculate the area of the base of the prism: The base is a rectangle measuring 10cm by 3cm: 3cm 10cm

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3cm 4cm 3cm 10cm Area of a rectangle = length x width Area = 10 x 3 Area = 30cm 2 We now know we can place 30 centimetre squares on the base of the prism. But we can also place 30 cubic centimetres on the base:

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10cm 3cm 4cm We have now got to find how many layers of 1cm cubes we can place in the prism: We can fit in 4 layers. Volume = 30 x 4 Volume = 120cm 3 That means that we can place 120 of our cubes measuring a centimetre in all directions inside our prism.

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10cm 3cm 4cm We have found that the volume of the cuboid is given by: Volume = 10 x 3 x 4 = 120cm 3 This gives us our formula for the volume of a prism: Volume = Area of Base x Height V=A base H for short.

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The Volume Of A Cylinder. Consider the cylinder below: 4cm 6cm It has a height of 6cm. What is the size of the radius ? 2cm Volume = A base x height What shape is the base? Circle Calculate the area of the circle: A = r 2 A = 3.14 x 2 x 2 A = 12.56 cm 2 Calculate the volume: V = r 2 x h V = 12.56 x 6 V = 75.36 cm 3 The formula for the volume of a cylinder is: V =A base x height = r 2 h r = radius h = height

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The Volume Of A Triangular Prism. Consider the triangular prism below: Volume = Abase x Height What shape is the base ? Triangle. Calculate the area of the triangle: 5cm 8cm 5cm A = (base x height)/2 A = (5 x 5)/2 A = 12.5cm 2 Calculate the volume: Volume = A base x Height V = 12.5 x 8 V = 100 cm 3 The formula for the volume of a triangular prism is : V = ½ b h h B= base h = height h = height

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What Goes In The Box ? 2 Calculate the volume of the shapes below: (1) 16cm 14cm (2) 3m 4m 5m (3) 6cm 12cm 8m 2813.4cm 3 30m 3 288cm 3

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