10-9 Volume of Cylinders

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10-8 Finding Volume6th HOMEWORK Answers

Page 536#1-6

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10-9 Volume of Cylinders6th Grade Math HOMEWORK

Page 540#1-3 and #6-8Due Monday!

Our Learning GoalStudents will be able to find the perimeter and area of polygons; find the area and circumference of circles and find the surface

area and volume of 3D shapes.

Our Learning Goal Assignments• Learn to find the perimeter and missing side lengths of a polygon.• Learn to estimate the area of irregular figures and to find the area

of rectangles, triangles, and parallelograms.• Learn to break a polygon into simpler parts to find its area.• Learn to make a model to explore how area and perimeter are

affected by changes in the dimensions of a figure.• Learn to identify the parts of a circle and to find the circumference

and area of a circle.• Learn to name solid figures.• Learn to find the surface areas of prisms, pyramids, and cylinders.• Learn to estimate and find the volumes of rectangular prisms and

triangular prisms.• Learn to find volumes of cylinders.

Today’s Learning Goal Assignment

Learn to find volumes of cylinders.

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10-9 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.

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10-9 Volume of Cylinders

Additional Example 1A: Finding the Volume of a Cylinder

Find the volume V of the cylinder to the nearest cubic unit.A.

Write the formula.Replace with 3.14, r with 4, and h with 7.Multiply.V 351.68

V = r2hV 3.14 42 7

The volume is about 352 ft3.Course 1

10-9 Volume of Cylinders

Try This: Example 1AFind the volume V of each cylinder to the nearest cubic unit.A.

Multiply.V 565.2The volume is about 565 ft3.

6 ft

5 ft

Write the formula.Replace with 3.14, r with 6, and h with 5.

V = r2hV 3.14 62 5

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10-9 Volume of Cylinders

Additional Example 1B: Finding the Volume of a Cylinder

B.

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 = r2hV 3.14 52 11

The volume is about 864 cm3.Course 1

10-9 Volume of Cylinders

Try This: Example 1BB.

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 = r2hV 3.14 42 6

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10-9 Volume of Cylinders

Additional Example 1C: Finding the Volume of a Cylinder

C.

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 = r2hV 3.14 72 9

The volume is about 1,385 in3.Course 1

10-9 Volume of Cylinders

Try This: Example 1CC.

Multiply.V 1230.88The volume is about 1231 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 = r2hV 3.14 72 8

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10-9 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.A. 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

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10-9 Volume of Cylinders

Additional Example 2B: Application

B. 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

__

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10-9 Volume of Cylinders

Try This: 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.A. 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

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10-9 Volume of Cylinders

Try This: Example 2BB. Ulysses’ 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 7.

22 7

__V 22 722

7 __

V = 88

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10-9 Volume of Cylinders

Additional Example 3A & 3B: 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.

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10-9 Volume of Cylinders

Try This: Example 3A & 3BFind 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.

10 cm2.5 cm

4 cm

4 cm

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10-9 Volume of Cylinders

Lesson QuizFind 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

1017 ft3

1,181.64 ft3

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10-9 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