12.5 Volume of Pyramids and Cones

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Presentation transcript:

12.5 Volume of Pyramids and Cones Chapter 12 12.5 Volume of Pyramids and Cones GOAL 1 Finding Volumes of Cones GOAL 2 Using Volumes in Real-Life Problems

Find the area of the base of the cone Base is a circle Area of Circle = r2 B = 36 in2

Theorem 12.9 Volume of a Cone B is the area of the base H is the height

Find the volume of each cone Area of the Base B = r2 = (4)2 = 16 Find the height h = 12 Fill in the formula

Find the volume of each cone Area of the base B = r2 = (5)2 = 25 Find the height From vertex perpendicular to base h2 + 52 = 82 h = 39 Fill in the formula

Find the volume of each cone Area of the base B = r2 = (9)2 = 81 Find the height From vertex perpendicular to base h2 + 92 = 212 h = 360 = 610 Fill in the formula

Applications To complete a construction job, a contractor needs 145 more cubic yards of concrete. If there remains a conical pile of concrete mix measuring 36 feet in diameter and 12 feet high, is there enough concrete still on the job site to finish the job? Explain your reasoning. How much does he have? (Find the volume or the pile) Convert feet to yards d = 12 yds, r = 6 yds, h = 4 yds Find the Volume Yes he has plenty

Applications The limestone blocks from which an ancient pyramid was made weigh about 2 tons per cubic yard. Find the approximate weight of the pyramid having a square base of length 250 yards and a height of 150 yards What is the volume (Use the formula for a pyramid) Find the weight (Multiply by 2) 3125000(2) = 6250000 tons

Find the volume of the solid Composed of two cones each with radius of 5. Need to find the height of each cone. Find the Volume of each cone Add the volumes together

First, find the volume of the left cone Find the height (pythagorean theorem) h2 + 52 = 102  h = 53 Find the Volume

Second, find the volume of the right cone Find the height (pythagorean theorem) h2 + 52 = 182  h = 299 Find the Volume

Now find the total Volume Volume of left cone: V  226.72 in3 Volume of Right Cone: V  452.69 in3 Total Volume: V  226.72 + 452.69 = 679.41in3

Homework #67 Pg 755-757 9, 17-19, 21, 25-37, 40-51