10-8
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10-8 Volume of Cylinders Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day
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Volume of Cylinders. 10-8. Course 1. Warm Up. Problem of the Day. Lesson Presentation. Volume of Cylinders. 10-8. 1,320 cm 3. 359.04 cm 3. Course 1. Warm Up Find the volume of each figure described. 1. rectangular prism with length 12 cm, width 11 cm, and height 10 cm. - PowerPoint PPT Presentation
Transcript of 10-8
10-8 Volume of Cylinders
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Warm UpFind the volume of each figure described.
Course 1
10-8 Volume of Cylinders
359.04 cm3
1,320 cm3
1. rectangular prism with length 12 cm, width 11 cm, and height 10 cm
2. triangular prism with height 11 cm and triangular base with base length 10.2 cm and height 6.4 cm
Problem of the Day
The height of a box is half its width. The length is 12 in. longer than its width. If the volume of the box is 28 in , what are the dimensions of the box?1 in. 2 in. 14 in.
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Course 1
10-8 Volume of Cylinders
Learn to find volumes of cylinders.
Course 1
10-8 Volume of Cylinders
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.
Course 1
10-8 Volume of Cylinders
Additional Example 1A: Finding the Volume of a Cylinder
Find the volume V of the cylinder to the nearest cubic unit.
Write the formula.
Replace with 3.14, r with 4, and h with 7.Multiply.V 351.68
V = r2h
V 3.14 42 7
The volume is about 352 ft3.
Course 1
10-8 Volume of Cylinders
Additional Example 1B: Finding the Volume of a Cylinder
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 = r2h
V 3.14 52 11
The volume is about 864 cm3.
Course 1
10-8 Volume of Cylinders
Additional Example 1C: Finding the Volume of a Cylinder
Find the radius.r = + 4h3__
r = + 4 = 793__ Substitute 9 for h.
Write the formula.
Replace with 3.14, r with 7, and h with 9.Multiply.V 1,384.74
V = r2h
V 3.14 72 9
The volume is about 1,385 in3.Course 1
10-8 Volume of Cylinders
Check It Out: Example 1A
Find the volume V of each cylinder to the nearest cubic unit.
Multiply.V 565.2
The volume is about 565 ft3.
6 ft
5 ft
Write the formula.
Replace with 3.14, r with 6, and h with 5.
V = r2h
V 3.14 62 5
Course 1
10-8 Volume of Cylinders
Check It Out: Example 1B
Multiply.V 301.44
8 cm ÷ 2 = 4 cm
The volume is about 301 cm3.
Find the radius.
8 cm
6 cm
Write the formula.
Replace with 3.14, r with 4, and h with 16.
V = r2h
V 3.14 42 6
Course 1
10-8 Volume of Cylinders
Check It Out: Example 1C
Multiply.V 1230.88
The volume is about 1,231 in3.
Find the radius.r = + 5h4__
r = + 5 = 784__ Substitute 8 for h.
r = + 5
h = 8 in
h4
Write the formula.
Replace with 3.14, r with 7, and h with 8.
V = r2h
V 3.14 72 8
Course 1
10-8 Volume of Cylinders
Additional Example 2A: Application Ali 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
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
10-8 Volume of Cylinders
Additional Example 2B: Application
Scott’s pencil holder
Write the formula.
Multiply.
4 in. ÷ 2 = 2 in.
The volume of Scott’s pencil holder is about 75 in3.
Find the radius.
V = r2h
Replace with , r with
2, and h with 6.
22 7
__V 22 622
7 __
V = 75 528 7
___ 37
__
Course 1
10-8 Volume of Cylinders
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
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
10-8 Volume of Cylinders
Check It Out: Example 2B
Ulysses’ pencil holder
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.
22 7
__V 22 722
7 __
V 88
Course 1
10-8 Volume of Cylinders
Additional Example 3: Comparing Volumes of Cylinders
Find which cylinder has the greater volume.
Cylinder 1:
V 3.14 1.52 12V = r2h
V 84.78 cm3
Cylinder 2:
V 3.14 32 6V = r2h
V 169.56 cm3
Cylinder 2 has the greater volume because 169.56 cm3 > 84.78 cm3.
Course 1
10-8 Volume of Cylinders
Check It Out: Example 3
Find which cylinder has the greater volume.
Cylinder 1:
V 3.14 2.52 10V = r2h
V 196.25 cm3
Cylinder 2:
V 3.14 22 4V = r2h
V 50.24 cm3
Cylinder 1 has the greater volume because 196.25 cm3 > 50.24 cm3.
Course 1
10-8 Volume of Cylinders
10 cm2.5 cm
4 cm
4 cm
Lesson Quiz: Part I
Find the volume of each cylinder to the nearest cubic unit. Use 3.14 for .
Insert Lesson Title Here
cylinder b
1,560.14 ft3
193 ft3
1,017 ft3
1,181.64 ft3
Course 1
10-8 Volume of Cylinders
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
Lesson Quiz: Part II
Insert Lesson Title Here
about 396 in2
Course 1
10-8 Volume of Cylinders
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 603 in2
