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California Standards

Learn and compare the volume formulas for triangular prisms, cylinders, and rectangular solid. Understand the similarity between them.

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California Standards

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  1. California Standards MG1.3 Know and usethe formulas for the volume of triangular prismsand cylinders (area of base × height);compare these formulas andexplain the similarity between them and the formula for the volume of a rectangular solid. Also covered:AF3.1, AF3.2

  2. To find the volume of a cylinder, you can use the same method as you did for prisms: multiply the area of the base by the height. V = Bh The area of the circular base is r2. V = r2h

  3. Write the formula. Replace with 3.14, r with 4, and h with 7. Multiply. V 351.68 V3.14427 The volume is about 352 ft3. Additional Example 1A: Finding the Volume of a Cylinder Find the volume V of the cylinder to the nearest cubic unit. V = r2h

  4. 10 cm ÷ 2 = 5 cm Find the radius. Write the formula. Replace with 3.14, r with 5, and h with 11. Multiply. V 863.5 V3.145211 The volume is about 864 cm3. Additional Example 1B: Finding the Volume of a Cylinder Find the volume V of the cylinder to the nearest cubic unit. V = r2h

  5. h 9 __ __ 3 3 V3.14729 V 1,384.74 Multiply. Replace with 3.14, r with 7, and h with 9. Write the formula. The volume is about 1,385 in3. r = + 4 = 7 r = + 4 Find the radius. Substitute 9 for h. Additional Example 1C: Finding the Volume of a Cylinder Find the volume V of the cylinder to the nearest cubic unit. V = r2h

  6. Multiply. V 565.2 The volume is about 565 ft3. Write the formula. Replace with 3.14, r with 6, and h with 5. V3.14625 Check It Out! Example 1A Find the volume V of the cylinder to the nearest cubic unit. 6 ft 5 ft V = r2h

  7. Multiply. V 301.44 8 cm ÷ 2 = 4 cm The volume is about 301 cm3. Find the radius. Write the formula. Replace with 3.14, r with 4, and h with 6. V3.14426 Check It Out! Example 1B 8 cm Find the volume V of the cylinder to the nearest cubic unit. 6 cm V = r2h

  8. h 8 __ __ 4 4 Write the formula. Replace with 3.14, r with 7, and h with 8. Substitute 8 for h. V3.14728 r = + 5 = 7 Find the radius. The volume is about 1,231 in3. V 1230.88 Multiply. r = + 5 Check It Out! Example 1C h r = + 5 Find the volume V of the cylinder to the nearest cubic unit. 4 h = 8 in. V = r2h

  9. Write the formula. Replace with 3.14, r with 1.5, and h with 5. Multiply. V 35.325 3 in. ÷ 2 = 1.5 in. V3.141.525 The volume of Ali’s pencil holder is about 35 in3. Find the radius. V = r2h Additional Example 2A: ApplicationAli has a cylinder-shaped pencil holder with a 3 in. diameter and a height of 5 in. Scott has a cylinder-shaped pencil holder with a 4 in. diameter and a height of 6 in. Estimate the volume of each cylinder to the nearest cubic inch. Ali’s pencil holder

  10. 3 528 22 22 __ ___ __ __ 7 7 7 7 Replace with , r with 2, and h with 6. V = r2h V 226 Find the radius. The volume of Scott’s pencil holder is about 75 in3. V = 75 4 in. ÷ 2 = 2 in. Multiply. Write the formula. Additional Example 2B: Application Scott’s pencil holder

  11. Write the formula. Replace with 3.14, r with 1.5, and h with 6. Multiply. V 42.39 3 in. ÷ 2 = 1.5 in. V3.141.526 The volume of Sara’s sunglasses case is about 42 in3. Find the radius. V =r2h Check It Out! Example 2A Sara has a cylinder-shaped sunglasses case with a 3 in. diameter and a height of 6 in. Ulysses has a cylinder-shaped pencil holder with a 4 in. diameter and a height of 7 in. Estimate the volume of each cylinder to the nearest cubic inch. Sara’s sunglasses case

  12. 22 22 __ __ 7 7 Write the formula. Multiply. 4 in. ÷ 2 = 2 in. The volume of Ulysses’ pencil holder is about 88 in3. Find the radius. V = r2h Replace with , r with 2, and h with 7. V 227 V 88 Check It Out! Example 2B Ulysses’ pencil holder

  13. Cylinder 2 has the greater volume because 169.56 cm3 > 84.78 cm3. V3.141.5212 V = r2h V 84.78 cm3 V3.14326 V =r2h V 169.56 cm3 Additional Example 3: Comparing Volumes of CylindersFind which cylinder has the greater volume. Cylinder 1: Cylinder 2:

  14. 10 cm 2.5 cm Cylinder 1 has the greater volume because 196.25 cm3 > 50.24 cm3. V3.142.5210 V = r2h V 196.25 cm3 V3.14224 V = r2h V 50.24 cm3 Check It Out! Example 3 Find which cylinder has the greater volume. Cylinder 1: 4 cm Cylinder 2: 4 cm

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