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

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Presentation transcript:

Surface Area of a 3-D solid

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

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.

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.

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 m m 2 = 196 m 2 Multiply sum by 2 = 196 m 2 x 2 = 392 m 2 The surface area = 392 m 2

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 cm 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 m 2 84 m 2 56 m 2

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

Top Right Side Front 10 cm 8 cm 5 cm Top Bottom Front Back Right Side Left 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 What is the Surface Area of the Rectangular solid? 340 cm 2

Find the Surface Area using a Formula S.A. = 2(area of the base) + (perimeter of the base) height S.A. = 2(2ft. X 3ft.) + (2ft + 3ft + 2ft + 3ft) x 6ft Answer: 72ft²

Surface Area of a Pyramid S.A. = Area of the base + 4(area of the triangular face) S.A. = 7ft x + 4(1/2 x 7ft x 8.7ft) S.A. = 49ft² ft² = 170.8ft²

Surface Area of a Cylinder S.A. = 2(Area of the base) + Circumference of the base x height of the cylinder S.A. = 2(3.14 x 10m²) + 20m x 3.14 x 13m S.A. = 628m² m² = m²

Now let’s do some practice problems! Pg. 568 #1-6 & Pg. 571 #1-3