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A prism is a solid whose sides (lateral sides) are parallelograms and whose bases are a pair of identical parallel polygons. A polygon is a simple closed figure whose sides are line segments. Bases Rectangular prismPentagonal prism Triangular prism

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The volume of a solid is the number of cubes it takes to fill the solid. The volume of a prism is found by multiplying the area of the base (B) by the height of the prism. The height is the distance between the 2 bases.

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Find the volume of a rectangular prism that has length of 7cm, with of 6 cm and height of 4 cm. 7 cm 6 cm 4 cm

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Steel weighs 0.28. What is the weight of a rectangular piece of steel 0.25 in. by 15.0 in. by 32.0 in?

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A cylinder is a geometric solid with a curved lateral surface. A can is an example of a cylinder. The volume of a cylinder is given by r h

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Example: Find the volume of the cylinder. d = 24 m 40 m Since d = 24, then r = 12 m.

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The volume of any cone or pyramid is given by the formula height Base Slant height diameter height Base where B = area of the base Apex

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Find the volume.

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19.6 cm

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The volume of a sphere is given by the formula

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The lateral surface area is the sum of the areas of the lateral faces of the prism. LSA = ph, where p is the perimeter of the base and h is the height of the prism.

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Find the lateral surface area of a rectangular prism that has length of 7cm, with of 6 cm and height of 4 cm. 7 cm 6 cm 4 cm Front and back = 4 x 7 each = 2(28) = 56 sq. cm. 2 ends = 4 x 6 each = 2(24) = 48 sq. cm. Lateral surface area = 104 sq. cm.

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The total surface area is found by finding the sum of the lateral area faces and the areas of the bases. TSA = ph + 2B 7 cm 6 cm 4 cm Lateral surface area = 104 sq. cm. The top and bottom are the bases. Top area = 6 x 7 = 42 sq. cm. Same for the bottom = 42 sq. cm Area of the bases = 2(42) = 84 sq. cm. Total S.A. = 104 + 84 = 188 sq. cm.

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The lateral surface area of a cylinder and be visualized by taking a can, cutting out the top and bottom, then down the side and unrolling the can. The resulting shape is a rectangle that has length equal to the circumference of the circular top and width equal to the height of the can. The formula is

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The total surface area is the sum of the lateral area and the 2 bases (top and bottom)

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Find the lateral surface area and total surface area of the cylinder. Lat. S.A.= Total S.A.= Lat.S.A. + 2 bases, where the bases are circles 2.5 in 12 in

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A steel cylindrical tank needs to hold 7000 gal. Due to space constraints, the tank should be 10 ft in diameter. How tall should the tank be? (Water weighs 8.34 lb/gal and 62.4 lb/cu.ft.) First convert gal to cu.ft. Take this volume and radius of 5 ft, substitute them into the volume formula and solve for h.

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Example continued:

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Find the amount of paper used for labels for 1000 cans like those shown below. 8.24 cm 3.16 cm Sweetheart Chicken Soup

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The total surface area of a sphere is given by TSA = 4πr²

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Lateral surface area of a cone is given by LSA = πrs, where r is the radius and s is the slant height, and the total surface area is given by TSA = πrs + πr²

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Find the lateral surface area and total surface area of a cone that has a radius of 6 ft, slant height of 10 ft and height of 8 ft.

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