Volume of cones and cylinders M 08 CG

Volume of cones and cylinders M 08. C-G. 3. 1. 1 Apply formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems. Formulas will be provided.

Warm-Up Evaluate the following expressions: 1) 2) 7 h 5 k for h = 2 and k = 10 2/5 (5)2(3) (substitute, then simplify exponent) 7(2)5(10) 2/5 (25) (3) = 7 (32) (10) = (10) (3) = 30 2240 3) What is the decimal approximation of ? Round to 2 decimal places.

Volume of Solids ● The volume of a solid is the amount of space that it contains. ● Since a solid has three dimensions, the units of volume are in cubic units (example, 7 cubic feet or 4. 25 in 3) ● For some solids, there are formulas to calculate the volume.

Cylinders: A cylinder is a solid that has two circular bases. The distance between these bases is called the height. The volume formula for a cylinder is where r is the radius of the base and h is the height of the cylinder.

1. Determine the volume of the cylinder below Write the formula. Substitute in. Get the answer and label.

1. Determine the volume of the cylinder below V= (8)2 (7) substitute V= (64) (7) simplify exponent V = 1407. 4 km 3 label your answer

2. Determine the volume of the cylinder below Write the formula. Substitute in. Get the answer and label.

2. Determine the volume of the cylinder below Write the formula. Substitute in. V V = (11)2(10) = (121) (10) = (1210) multiply = 3801. 3 ft 3 label answer

3. Determine the volume of the cylinder below. Show your steps.

3. Determine the volume of the cylinder below. V V = ( 5 ) 2( 4 ) = (25) (4) = (100) = 314. 2 in 3

Evaluate: 5 a 4 b 3 for a = 2 and b = 4

Evaluate: ¼ c 2 d + 3 d 3 for c = 5 and d = 8

Evaluate: ●

Evaluate: 4 a 3 + 2 b 2 - c 4 for a = 5, b = 10 and c = 2

Evaluate: 4 e 4 – 2 f f 3 for e = 3 and f = 2

Evaluate: 2 a + 4 b 4 for a = 6 and b = 2 2 + a 2

Volume of a Cone The volume of a cone is ⅓rd the volume of a cylinder with the same radius and height. Therefore, the volume of a cone is given by the formula

4. Determine the volume of the cone below

5. Determine the volume of the cone below

Your turn! 6. Determine the volume of the cone shown