Chapter 1212.4

Volume of Prisms and Cylinders

Volume of a Cylinder• Theorem 12.8: Volume of a Cylinder

– The volume V of a Cylinder is V = Bh = r2h, where B is the area of the base (a circle), h is the height, and r is the radius.

1. Area of Base: A = (4)2

• Base is a circle

2. Height: h = 11

• Distance between bases

3. Volume: V = (16)11 = 176 in3

Find the volume of the following cylinders

1. Base is a circle with radius 8.1

• B = (8.1)2 = 65.61

2. h = 10

3. V = (65.61)10 = 656.1

1. Base is a circle with radius 3

• B = (3)2 = 9

2. h = 12

3. V = (9)12 = 108

Find the Volume of the Cylinder

1. Base is a circle with radius 4

• B = (4)2 = 16

2. h = 9.5

3. V = (16)9.5 = 152

Solve for the variable using the given measurements. The prisms and

cylinders are right

1. The solid is a right rectangular prism

• V = Bh, B = 15(5), h = x

2. Fill in the information

• 525 = 15(5)x

3. Solve for x

• x = 7

Solve for the variable using the given measurements. The prisms and

cylinders are right

1. The solid is a right cylinder

• V = Bh = r2h, r = 8, h = x

2. Fill in the information

• 2420 = (8)2x

3. Solve for x

• x 12

Solve for the variable using the given measurements. The prisms and

cylinders are right.

1. The solid is a right triangular prism

• V = Bh, B is the area of the triangle

2. Fill in the information

• 455 = ½(10)(14)x

3. Solve for x

• x = 6.5

Make a sketch of the solid and find its volume

13. A prism has a square base with 5 foot sides and a height of 2.5 feet.

5 ft

2.5 ft

1. The solid is a square based prism

• V = Bh, B = 52

2. Find the Height

• h = 2.5

3. Substitute and find the volume

• V = 52(2.5) = 62.5 ft3

Make a sketch of the solid and find its volume

14. A cylinder has a diameter of 23 inches and a height of 16 inches.

16

11.5

1. Base is a circle with radius 11.5

• B = (11.5)2 = 132.25

2. h = 16

3. V = (132.25)16 = 2116 in3

15. Pillars How much plaster of paris is needed to make four miniature pillars for a model home if the pillars are regular hexagonal prisms with a height of

12 in. and base edges of 2 in.?

1. Base is a hexagon with s = 2

• a = 3

• 362632

1

2

1 ansB

2. h = 12

3. V = (6 3)12 = 723 in3

4. Since there are 4 pillars you need to multiply by 4

• Amount = 4(723) = 2883 in3

Homework #65Pg 747 – 749 16-18, 22-24, 26,

28-33, 39-49, 51-60