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Volume of Solids (2)

Volume of Solids (2). Today’s lesson will cover… finding volume of cylinders and cones using formulas to solve problems involving volume of prisms and cubes. What we must first know. Proportions and ratios. How to calculate the area of a circle. Definition of Volume.

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Volume of Solids (2)

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  1. Volume of Solids (2) Today’s lesson will cover… finding volume of cylinders and cones using formulas to solve problems involving volume of prisms and cubes.

  2. What we must first know Proportions and ratios How to calculate the area of a circle. Definition of Volume the amount of 3-dimensional space occupied by an object

  3. Cylinders • The bases of cylinders are circles. To find the area of the base use pi*r2 • After you find the base area (B), multiply by the height to get the volume • Volume of Cylinder = Bh Base area height

  4. Cylinders • Find the volume of the soda can shown below Calculate the area of the base A = 3.14*(2.75)2 A = 3.14*7.5625 A =23.746 square inches 5 inches Multiply base area times height 23.746 in2 * 5 in 118.73 in3 2 ¾ inches

  5. Mr. Emory bought a 5 gallon bucket of roof sealant for the house his construction class was building. The dimensions of the bucket are shown below. Using 1 gallon = 231 cubic inches, determine the depth of sealant in the bucket if there were 808 cubic inches left over. • Given information • 1 gallon = 231 cubic inches • 5 gallon bucket • 808 cubic inches left over • Diameter = 11.5 inches • Height of cylinder = 14.5 inches • Question • What is the depth (height) of the fluid remaining in the bucket. 14.5 in 11.5 in

  6. Mr. Emory bought a 5 gallon bucket of roof sealant for the house his construction class was building. The dimensions of the bucket are shown below. Using 1 gallon = 231 cubic inches, determine the depth of sealant in the bucket if there were 808 cubic inches left over. 1st determine the volume remaining • Full bucket – left over = amount used 1155in3-808 in3 Volume remaining = 347 in3 2nd find the area of the base Area of circle = πr2 = (3.14)(11.5/2)2 = 103.82 in2

  7. Mr. Emory bought a 5 gallon bucket of roof sealant for the house his construction class was building. The dimensions of the bucket are shown below. Using 1 gallon = 231 cubic inches, determine the depth of sealant in the bucket if there were 808 cubic inches left over. Now we can find the height by using the Volume formula for a cylinder V = Bh 347 in3 = 103.82 in2 * h h = 3.34 inches

  8. Cones • The base of a cone is a circle. To find the area of the base use pi*r2 • After you find the base area (B), multiply by 1/3 and by the height to get the volume • Volume of Cone = 1/3 Bh Base area

  9. Find the area of a cone with a 6 inch radius and 5 inch height • Volume = 1/3*B*h • B = 3.14(6in)2 = 113.04 in2 • h = 5 inches • V = 1/3 * 113.04 in2*5in • V = 118.4 in3

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