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Learn to estimate and find the volumes of rectangular prisms and cylinders.

Volume of Prisms. 10-7. Course 1. Learn to estimate and find the volumes of rectangular prisms and cylinders. Volume of Prisms. 10-7. Course 1. Insert Lesson Title Here. Vocabulary. volume. Volume of Prisms. 10-7. Course 1. Volume is the number of cubic units needed to fill a space.

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Learn to estimate and find the volumes of rectangular prisms and cylinders.

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  1. Volume of Prisms 10-7 Course 1 Learn to estimate and find the volumes of rectangular prisms and cylinders.

  2. Volume of Prisms 10-7 Course 1 Insert Lesson Title Here Vocabulary volume

  3. Volume of Prisms 10-7 Course 1 Volume is the number of cubic units needed to fill a space.

  4. Volume of Prisms 10-7 Course 1 It takes 10, or 5 · 2, centimeter cubes to cover the bottom layer of this rectangular prism. There are 3 layers of 10 cubes each to fill the prism. It takes 30, or 5 · 2 · 3, cubes. Volume is expressed in cubic units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cm3.

  5. Volume of Prisms 10-7 Course 1 To find the volume of any prism, you can use the formula V= Bh, where B is the area of the base, and h is the prism’s height. So, to find the volume of a rectangular prism, B is the area of the rectangular base (lw) and h is the height of the prism.

  6. Volume of Prisms 10-7 Course 1 V = Bh V = lwh Write the formula. V = 26•11•13 l = 26; w = 11; h = 13 V = 3,718 in3 Multiply.

  7. Volume of Prisms 10-7 Course 1 V = Bh V = lwh Write the formula. V = 29•12•16 l = 29; w = 12; h = 16 V = 5,568 in3 Multiply.

  8. Volume of Prisms 10-7 Caution! The bases of a prism are always two congruent, parallel polygons. Course 1

  9. Volume of Cylinders 10-8 Course 1 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. volume of a cylinder = area of base  height The area of the circular base is r2, so the formula is V = Bh = r2h.

  10. QUICK REVIEW • Diameter is the length across a circle going through the center point • Radius is half the diameter – or half the length across a circle going through the center point. • So, 2r = d • And, d/2 = r

  11. I’ll give you one, you tell me the other • If the radius is 6, the diameter is: • If the diameter is 8, the radius is: • If the radius is 12, the diameter is: • If the diameter is 10, the radius is: • If the diameter is 9, the radius is: • If the diameter is 4, the radius is:

  12. LET’S MAKE THINGS EASIER • Pi is a really long number • It is literally the ratio of the diameter of a circle to it’s circumference. YOU DO NOT NEED TO KNOW THAT. • But, we are going to round 3.14 to something easier. What is the nearest whole number? • Use 3 for pi

  13. Volume of Cylinders 10-8 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. Course 1 Additional Example 1A: Finding the Volume of a Cylinder Find the volume V of the cylinder to the nearest cubic unit. V = r2h

  14. Volume of Cylinders 10-8 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. Course 1 Additional Example 1B: Finding the Volume of a Cylinder V = r2h

  15. Volume of Cylinders 10-8 h 9 __ __ 3 3 Replace with 3.14, r with 7, and h with 9. Find the radius. r = + 4 r = + 4 = 7 Write the formula. V 1,384.74 Multiply. V3.14729 The volume is about 1,385 in3. Substitute 9 for h. Course 1 Additional Example 1C: Finding the Volume of a Cylinder V = r2h

  16. Volume of Cylinders 10-8 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 Course 1 Check It Out: Example 1A Find the volume V of each cylinder to the nearest cubic unit. 6 ft 5 ft V = r2h

  17. Volume of Cylinders 10-8 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 16. V3.14426 Course 1 Check It Out: Example 1B 8 cm 6 cm V = r2h

  18. Volume of Cylinders 10-8 8 h __ __ 4 4 Write the formula. Replace with 3.14, r with 7, and h with 8. V3.14728 r = + 5 Substitute 8 for h. Multiply. V 1230.88 r = + 5 = 7 The volume is about 1,231 in3. Find the radius. Course 1 Check It Out: Example 1C h r = + 5 4 h = 8 in V = r2h

  19. Volume of Cylinders 10-8 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 Course 1 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

  20. Volume of Cylinders 10-8 3 528 22 22 __ __ ___ __ 7 7 7 7 V = r2h Write the formula. V = 75 Find the radius. 4 in. ÷ 2 = 2 in. V 226 The volume of Scott’s pencil holder is about 75 in3. Replace with , r with 2, and h with 6. Multiply. Course 1 Additional Example 2B: Application Scott’s pencil holder

  21. Volume of Cylinders 10-8 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 Course 1 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

  22. Volume of Cylinders 10-8 22 22 __ __ 7 7 Replace with , r with 2, and h with 7. V 88 Write the formula. Multiply. Find the radius. V 227 The volume of Ulysses’ pencil holder is about 88 in3. V = r2h 4 in. ÷ 2 = 2 in. Course 1 Check It Out: Example 2B Ulysses’ pencil holder

  23. Volume of Cylinders 10-8 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 Course 1 Additional Example 3: Comparing Volumes of CylindersFind which cylinder has the greater volume. Cylinder 1: Cylinder 2:

  24. Volume of Cylinders 10-8 10 cm 2.5 cm 4 cm 4 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 Course 1 Check It Out: Example 3 Find which cylinder has the greater volume. Cylinder 1: Cylinder 2:

  25. Volume of Cylinders 10-8 1,017 ft3 193 ft3 1,181.64 ft3 1,560.14 ft3 Course 1 Insert Lesson Title Here Lesson Quiz: Part I Find the volume of each cylinder to the nearest cubic unit. Use 3.14 for . 1. radius = 9 ft, height = 4 ft 2. radius = 3.2 ft, height = 6 ft • 3. Which cylinder has a greater volume? • a. radius 5.6 ft and height 12 ft • b. radius 9.1 ft and height 6 ft cylinder b

  26. Volume of Cylinders 10-8 Course 1 Insert Lesson Title Here Lesson Quiz: Part II 4. Jeff’s drum kit has two small drums. The first drum has a radius of 3 in. and a height of 14 in. The other drum has a radius of 4 in. and a height of 12 in. Estimate the volume of each cylinder to the nearest cubic inch. a. First drum b. Second drum about 396 in2 about 603 in2

  27. Volume of Prisms 10-7 3,600 cm3 Course 1 Insert Lesson Title Here Lesson Quiz Find the volume of each figure. 1. rectangular prism with length 20 cm, width 15 cm, and height 12 cm

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