Chapter 12 12.4

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 =  r 2 h, 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  in 3

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 =  r 2 h, r = 8, h = x 2. Fill in the information • 2420 =  (8) 2 x 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.

1. The solid is a square based prism • V = Bh, B = 5 2 2.5 ft 5 ft 2. Find the Height • h = 2.5

3. Substitute and find the volume • V = 5 2 (2.5) = 62.5 ft 3

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 1. Base is a circle with radius 11.5

• B = (11.5) 2  = 132.25

 2. h = 16 3. V = (132.25

 )16 = 2116  in 3 11.5

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 • •

B

a =  3  1 2

ans

 1 2       6 2. h = 12 3. V = (6  3)12 = 72  3 in 3 3 4. Since there are 4 pillars you need to multiply by 4 • Amount = 4(72  3) = 288  3 in 3

Homework #65 Pg 747 – 749 16-18, 22-24, 26, 28-33, 39-49, 51-60