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

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

Cylinders The bases of cylinders are circles. To find the area of the base use pi*r 2 The bases of cylinders are circles. To find the area of the base use pi*r 2 After you find the base area (B), multiply by the height to get the volume After you find the base area (B), multiply by the height to get the volume Volume of Cylinder = Bh Volume of Cylinder = Bh Base area height

Cylinders Find the volume of the soda can shown below Find the volume of the soda can shown below 5 inches 2 ¾ inches Calculate the area of the base A = 3.14*(2.75) 2 A = 3.14* A = square inches Multiply base area times height in 2 * 5 in in 3

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 Given information 1 gallon = 231 cubic inches 1 gallon = 231 cubic inches 5 gallon bucket 5 gallon bucket 808 cubic inches left over 808 cubic inches left over Diameter = 11.5 inches Diameter = 11.5 inches Height of cylinder = 14.5 inches Height of cylinder = 14.5 inches Question Question What is the depth (height) of the fluid remaining in the bucket. What is the depth (height) of the fluid remaining in the bucket in 14.5 in

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. 1 st determine the volume remaining Full bucket – left over = amount used Full bucket – left over = amount used 1155in in 3 Volume remaining = 347 in 3 2 nd find the area of the base Area of circle = πr 2 = (3.14)(11.5/2) 2 = in 2

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 in 3 = in 2 * h h = 3.34 inches

Cones The base of a cone is a circle. To find the area of the base use pi*r 2 The base of a cone is a circle. To find the area of the base use pi*r 2 After you find the base area (B), multiply by 1/3 and by the height to get the volume 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 Volume of Cone = 1/3 Bh Base area

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