12.5 volumes of pyramids and cones ink.notebook volumes of...12.5 volumes of pyramids and cones...
Transcript of 12.5 volumes of pyramids and cones ink.notebook volumes of...12.5 volumes of pyramids and cones...
12.5 volumes of pyramids and cones ink.notebook
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May 01, 2018
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12.5 Volume of Pyramids and Cones
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Lesson Objectives Standards Lesson Notes
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12.5 Volumes of Pyramids and Cones
Lesson Objectives
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Lesson NotesStandards
After this lesson, you should be able to successfully find the volumes of pyramidsand cones.
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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 Pyramids This figure shows a prism and a pyramid that have the same base and the same height. It is clear that the volume of the pyramid is less than the volume of the prism. More specifically,the volume of the pyramid is ____________ of the volume of the prism.
Volume of a Pyramid
Or Volume of Pyramid = (Area of Base)(height of pyramid) ÷ 3
If a pyramid has a volume of V cubic units, a height of h units, and a base with an area of B square units, then
12.5 volumes of pyramids and cones ink.notebook
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Find the volume of each pyramid. Round to the nearest tenth if necessary.
1. 2.
Find area of base carefully.
3. 4.Find the volume of each pyramid. Round to the nearest tenth if necessary.
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5. 6.Find the volume of each pyramid. Round to the nearest tenth if necessary.
Volumes of Cones For a cone, the volume is onethird the product of the height and the area of the base. The base of a cone is a circle, so the area of the base is πr2.
If a cone has a volume of V cubic units, a height of h units, and the bases have a radius of r units, then
Volume of a Cone
Or Volume of cone = (πr2h) ÷ 3
Find the volume of each cone. Round to the nearest tenth.
7. 8.
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Find the volume of each cone. Round to the nearest tenth.9. 10.
On the Worksheet
HOMEWORK12.5 Practice WS on Volumes of Pyramids and Cones
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Find the volume of each pyramid or cone. Round to the nearest tenth if necessary.
1. 2.
Find the volume of each pyramid or cone. Round to the nearest tenth if necessary.
3. 4.
Find the volume of each pyramid or cone. Round to the nearest tenth if necessary.
5. 6.
Find the volume of each oblique pyramid or cone. Round to the nearest tenth if necessary.
7. 8.
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9. CONSTRUCTION Mr. Ganty built a conical storage shed. The base of the shed is 4 meters in diameter and the height of the shed is 3.8 meters. What is the volume of the shed?
10. HISTORY The start of the pyramid age began with King Zoser's pyramid, erected in the 27th century B.C. In its original state, it stood 62 meters high with a rectangular base that measured 140 meters by 118 meters. Find the volume of the original pyramid.
11. ICE CREAM DISHES The part of a dish designed for ice cream is shaped like an upsidedown cone. The base of the cone has a radius of 2 inches and the height is 1.2 inches.
What is the volume of the cone? Round your answer to the nearest hundredth.
12. GREENHOUSES A greenhouse has the shape of a square pyramid. The base has a side length of 30 yards. The height of the greenhouse is 18 yards.
What is the volume of the greenhouse?
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13. TEEPEE Caitlyn made a teepee for a class project. Her teepee had a diameter of 6 feet. The angle the side of the teepee made with the ground was 65.What was the volume of the teepee? Round your answer to the nearest hundredth. What is the volume of the stone that the sculptor must remove?
Round your answer to the nearest hundredth.
14. SCULPTING A sculptor wants to remove stone from a cylindrical block 3 feet high and turn it into a cone. The diameter of the base of the cone and cylinder is 2 feet.
1. 66.7 ft3 3. 357.8 in3 5. 1230.9 yd3
7. 32 ft3 9. 15.9 m3 11. 5.02 in3 13. 60.57 ft3
Answers: