Holt CA Course 1 10-9 Volume of Cylinders MG1.3 Know and use the formulas for the volume of...
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Holt CA Course 1 10-9 Volume of Cylinders MG1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid. Also covered: AF3.1, AF3.2 California Standards
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Transcript of Holt CA Course 1 10-9 Volume of Cylinders MG1.3 Know and use the formulas for the volume of...
Holt CA Course 1
10-9 Volume of Cylinders
MG1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.Also covered: AF3.1, AF3.2
California Standards
Holt CA Course 1
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.
V = Bh
The area of the circular base is r2.
V = r2h
Holt CA Course 1
10-9 Volume of CylindersAdditional 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.
Holt CA Course 1
10-9 Volume of CylindersAdditional 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.
Find the volume V of the cylinder to the nearest cubic unit.
Holt CA Course 1
10-9 Volume of CylindersAdditional 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.
Find the volume V of the cylinder to the nearest cubic unit.
Holt CA Course 1
10-9 Volume of CylindersCheck It Out! Example 1A
Find the volume V of the 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
Holt CA Course 1
10-9 Volume of CylindersCheck 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 6.
V = r2h
V 3.14 42 6
Find the volume V of the cylinder to the nearest cubic unit.
Holt CA Course 1
10-9 Volume of CylindersCheck 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
Find the volume V of the cylinder to the nearest cubic unit.
Holt CA Course 1
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.
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
Holt CA Course 1
10-9 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
__
Holt CA Course 1
10-9 Volume of CylindersCheck 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
Holt CA Course 1
10-9 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
Holt CA Course 1
10-9 Volume of CylindersAdditional 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.
Holt CA Course 1
10-9 Volume of CylindersCheck 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.
10 cm2.5 cm
4 cm
4 cm
