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Chapter 10

Chapter 10. Volume and Surface Area. (Not in the book.). A Review of Area. Area Formulas. Triangle Square Rectangle Parallelogram Trapezoid. Area Challenge. With your group, complete Sheet 1 together. You may use the Formula Cards provided to assist you.

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Chapter 10

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  1. Chapter 10 Volume and Surface Area

  2. (Not in the book.) A Review of Area

  3. Area Formulas • Triangle • Square • Rectangle • Parallelogram • Trapezoid

  4. Area Challenge • With your group, complete Sheet 1 together. • You may use the Formula Cards provided to assist you. • When you are finished with that side, you must have it checked for accuracy before moving on to Sheet 2. • With your group, complete Sheet 2. • When you are finished with Sheet 2, raise your hand to let your teacher know your table is ready. • If Sheet 2 is correct, you will receive Sheet 3 – applying this skill to a real life situation. • With your group, complete Sheet 3. Raise your hand to have your paper checked. THERE WILL BE A SMALL TREAT FOR THOSE GROUPS WHO CAN ALLFINISH SHEET THREE CORRECTLYBEFORE CLASS IS OVER.

  5. Prisms and Pyramids Volume

  6. Volume of Prisms • A prism is a three-dimensional figure with at least three rectangular lateral faces and top and bottom faces that are parallel. • The volumeof a three-dimensional figure is the measure of space it occupies. • It is measured in CUBIC UNITS. • A rectangular prism is a prism that has rectangular bases.

  7. Rectangular Prism Practice • Find the volume of each prism. • A concession stand serves peanuts in two different containers. Which container holds more peanuts? Justify your answer. 142.5 m3 24 cm3 Box B holds more peanuts. Box A: 61.25 in3 Box B: 73 in3

  8. Volume of Prisms • A triangular prism is a prism that has triangular bases. Triangular Prism Practice 70 in3 46.8 mm3

  9. Volume of Pyramids • A pyramidis a three-dimensional figure with one base and triangular lateral faces, or any flat surfaces that are not bases.

  10. Pyramid Practice • Find the volume of the pyramid. Round to the nearest tenth. • 9.7 in3 • A triangular pyramid has a volume of 60 cubic centimeters. The triangular base has a 12-centimeter base and a 5-centimeter height. Find the height of the pyramid. • 6 cm • A scale model of the Egyptian pyramidis shown. Find the volume of the square pyramid. • 216 in3

  11. Prisms and Pyramids Surface Area

  12. Surface Area of Prisms • The sum of the areas of all the surfaces, or faces, of a three-dimensional figure is the surface area. • HOW DO WE DO THAT? • Find the AREA of each FACE. • ADD all the AREAS together. • You may need to look back in your notes for area formulas. EXAMPLE Find the surface area of the rectangular prism. top and bottom: 2(5×4) = 40 front and back: 2(5×3) = 30 two sides: 2(3×4) = 24 Sum of the ALL the AREAS: 94 square centimeters

  13. Prism Practice • Find the surface area of each prism. • If one gallon of paint covers 350 square feet, will 8 gallons of paint be enough to paint the inside and outside of the fence shown? EXPLAIN. 216 m2 864 mm2 385.28 mm2 195 in2 Yes. 2520 ft2 < 2800 ft2

  14. Surface Are of Pyramids • A right square pyramid has a square base and four isosceles triangles that make up the lateral faces. • The height of each lateral face is called the slant height (𝓁). • The lateral surface area (L) of a solid is the sum of the areas of all its lateral faces. • Total Surface Area of a Regular Pyramid:

  15. Pyramid Examples

  16. Pyramid Practice • Find the total surface area of the pyramid. Round to the nearest tenth. • 41 in2 • Find the total surface area of the pyramid with a base area of 84.5 square centimeters. • 484.1 cm2 • A game piece for a board game is shaped like a square pyramid. It has a slant height of 15 millimeters and the bases have edges 11 millimeters long. What is the surface area of the game piece? • 451 mm2

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