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Surface Area and Volume Calculations for Playhouse and Geometric Figures

Learn how to calculate the surface area and volume of a playhouse, as well as various geometric figures such as prisms, cylinders, pyramids, cones, and spheres. Includes step-by-step examples and formulas.

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Surface Area and Volume Calculations for Playhouse and Geometric Figures

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  1. Warm UP The playhouse is a composite figure with a floor and no windows. What is the surface area of the playhouse?

  2. 2 Make a Plan Additional Example 3 Continued Draw nets of the figures and shade the parts that show the surface area of the playhouse.

  3. The surface area of a sphere is four times the area of a great circle.

  4. Additional Example 2: Finding Surface Area of a Sphere Find the surface area, both in terms of p and to the nearest tenth. Use 3.14 for p. Surface area of a sphere S = 4pr2 = 4p(32) Substitute 3 for r. = 36p in2 113.0 in2

  5. Learn to find the volume of prisms and cylinders.

  6. Remember! Area is measured in square units. Volume is measured in cubic units.

  7. Additional Example 1A: Finding the Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. Use 3.14 for . a rectangular prism with base 2 cm by 5 cm and height 3 cm B = 2 • 5 = 10 cm2 Area of base Volume of a prism V = Bh = 10 • 3 = 30 cm3

  8. Additional Example 1B: Finding the Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. Use 3.14 for . B =  (42) = 16in2 Area of base 4 in. Volume of a cylinder V = Bh 12 in. = 16• 12 = 192  602.9 in3

  9. 1 2 B = • 6 • 5 = 15 ft2 Additional Example 1C: Finding the Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. Use 3.14 for . Area of base 5 ft V = Bh Volume of a prism = 15 • 7 = 105 ft3 7 ft 6 ft

  10. Warm UP (You can use a calculator) Find the volume of each figure to the nearest tenth. Use 3.14 for . 10 in. 1. 3. 2 in. 2. 12 in. 12 in. 10.7 in. 15 in. 3 in. 8.5 in. 942 in3 160.5 in3 306 in3 4. Explain whether doubling the radius of the cylinder above will double the volume. No; the volume would be quadrupled because you have to use the square of the radius to find the volume.

  11. Learn to find the volume of pyramids and cones.

  12. B = (4 • 7) = 14 cm2 1 3 1 2 1 3 V = Bh V = • 14 • 6 Additional Example 1A: Finding the Volume of Pyramids and Cones Find the volume of the figure. Use 3.14 for p. V = 28 cm3

  13. 1 3 1 3 V = Bh V = • 9 • 10 Additional Example 1B: Finding the Volume of Pyramids and Cones Find the volume of the figure. Use 3.14 for p. B = (32) = 9 in2 V = 30 94.2 in3 Use 3.14 for .

  14. B = (5 • 7) = 17.5 in2 1 3 1 2 1 3 V = Bh V = • 17.5 • 7 Check It Out: Example 1A Find the volume of the figure. Use 3.14 for p. 7 in. 5 in. 7 in. V  40.8 in3

  15. Learn to find the volume and surface area of spheres.

  16. A sphere is the set of points in three dimensions that are a fixed distance from a given point, the center. A plane that intersects a sphere through its center divides the two halves or hemispheres. The edge of a hemisphereis agreat circle.

  17. 4 3 V = pr3 = p(12)3 4 3 Additional Example 1: Finding the Volume of a Sphere Find the volume of a sphere with radius 12 cm, both in terms of p and to the nearest tenth. Use 3.14 for p. Volume of a sphere Substitute 12 for r. = 2304p cm3 7,234.6 cm3

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