Transcript Document 1063754
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