12.4 volumes of prisms and cylinders ink.notebook · 12.4 volumes of prisms and cylinders...
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12.4 volumes of prisms and cylinders ink.notebook
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12.4 Volume of Prisms and Cylinders
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Lesson Objectives Standards Lesson Notes
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12.4 Volumes of Prisms and Cylinders
12.4 volumes of prisms and cylinders ink.notebook
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April 26, 2018
Lesson Objectives
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Lesson NotesStandards
After this lesson, you should be able to successfully find the volumes of prisms and cylinders.
Lesson Objectives Standards Lesson NotesG.MG.1 Use geometric shapes, their measures, and their properties to describe objects.G.GMD.4 Identify the shapes of twodimensional cross sections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects.G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.G.MG.2 Apply concepts of density based on area and volume in modeling situations.
Volumes of Prisms The measure of the amount of space that a threedimensional figure encloses is the volume of the figure. Volume is measured in units such as cubic feet, cubic yards, or cubic meters. One cubic unit is the volume of a cube that measures one unit on each edge.
If a prism has a volume of V cubic units, a height of h units, and each base has an area of B square units, then V = Bh. Volume = (Area of the Base)(height of prism)
1. Find the volume of the prism.
V = Bh
The volume of the prism is _____ cm3
12.4 volumes of prisms and cylinders ink.notebook
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2. 3.
Find the volume of each prism.
4. 5.
Find the volume of each prism.
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Volumes of Cylinders The volume of a cylinder is the product of the height and the area of the base. When a solid is not a right solid, use Cavalieri's Priniciple to find the volume. The principle states that if two solids have the same height and the same cross sectional area at every level, then they have the same volume.
Volume of a CylinderIf a cylinder has a volume of V cubic units, a height of h units, and the bases have a radius of r units, then
V = πr2h. Volume = (Area of circle)(height of cylinder)
Height = ____________
6. Find the volume of the oblique cylinder.
Use the Pythagorean Theorem to find the height of the cylinder.
The Volume is about __________ cubic inches.
V = πr2h
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Find the volume of each cylinder.
7. 8.
Find the volume of each cylinder.
9. 10.
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11. The Meyer family uses a kitchen trash can shaped like a cylinder. It has a height of 18 inches and a base diameter of 12 inches. What is the volume of the trash can? Round your answer to the nearest tenth of a cubic inch.
On the Worksheet
HOMEWORK12.4 Practice on Volumes of Prisms and Cylinders
12.4 volumes of prisms and cylinders ink.notebook
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Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
1. 2.
Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
3. 4.
Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
5. 6.
Find the volume of each prism or cylinder. Round to the nearest tenth if necessary.
7. 8.
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Find the volume of each oblique prism or cylinder. Round to the nearest tenth if necessary.
9. 10.
Find the volume of each oblique prism or cylinder. Round to the nearest tenth if necessary.
11. 12.
13. AQUARIUM Mr. Gutierrez purchased a cylindrical aquarium for his office. The aquarium has a height of
a radius of 21 inches.inches and
a) What is the volume of the aquarium in cubic feet?
b) If there are 7.48 gallons in a cubic foot, how many gallons of water does the aquarium hold?
c) If a cubic foot of water weighs about 62.4 pounds, what is the weight of the water in the aquarium to the nearest five pounds?
14. BENCH Inside a lobby, there is a piece of furniture for sitting. The furniture is shaped like a simple block with a square base 6 feet on each side and a height of feet.
What is the volume of the seat?
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15. PENCIL GRIPS A pencil grip is shaped like a triangular prism with a cylinder removed from the middle. The base of the prism is a right isosceles triangle with leg lengths of 2 centimeters. The diameter of the base of the removed cylinder is 1 centimeter. The heights of the prism and the cylinder are the same, and equal to 4 centimeters.
What is the exact volume of the pencil grip?a) What will the volume of the tunnel be?
b) If instead of a rectangular shape, the tunnel had a semicircular shape with a 50foot diameter, what would be its volume? Round your answer to the nearest cubic foot.
16. TUNNELS Construction workers are digging a tunnel through a mountain. The space inside the tunnel is going to be shaped like a rectangular prism. The mouth of the tunnel will be a rectangle 20 feet high and 50 feet wide and the length of the tunnel will be 900 feet.
1. 2304 cm3 3. 90 m3 5. 96.8 in3 7. 16249.5 mm3
9. 1224 cm3 11. 6028.8 cm3
13.a) 20.4 ft3 b) 152.6 gal c) 1275 lb 15. 8 π cm3
Answers: