Unit 3: Geometric Applications of Exponents

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Unit 3: Geometric Applications of Exponents Volume of Cylinders Unit 3: Geometric Applications of Exponents

A cylinder is a three-dimensional figure that has two congruent circular bases. Height Base

Volume of Cylinders K (Key Word) I (Information) M (Memory Cue) Cylinder The volume of a cylinder is the area of the base B times the height h. V = Bh = (r2)h Area is measured in square units. Volume is measured in cubic units.

V = Bh = r2h Volume of Cylinders - To find the volume of a cylinder, multiply the area of the base by the height. volume of a cylinder = area of base  height The area of the circular base is r2 V = Bh = r2h

Volume of Cylinders Find the volume V of the cylinder to the nearest cubic unit. V = r2h Write the formula. V  3.14  42  7 Replace  with 3.14, r with 4, and h with 7. V  351.68 Multiply. The volume is about 352 ft3.

Volume of Cylinders Find the volume V of the cylinder to the nearest cubic unit. 10 cm ÷ 2 = 5 cm Find the radius. V = r2h Write the formula. V  3.14  52  11 Replace  with 3.14, r with 5, and h with 11. V  863.5 Multiply. The volume is about 864 cm3.

Volume of Cylinders A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling the height of the can would have the same effect on the volume as tripling the radius. By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.

Volume of Cylinders Find the volume V of each cylinder to the nearest cubic unit. 6 ft 5 ft V = r2h Write the formula. V  3.14  62  5 Replace  with 3.14, r with 6, and h with 5. V  565.2 Multiply. The volume is about 565 ft3.

Volume of Cylinders 8 cm 6 cm 8 cm ÷ 2 = 4 cm Find the radius. V = r2h Write the formula. V  3.14  42  6 Replace  with 3.14, r with 4, and h with 16. V  301.44 Multiply. The volume is about 301 cm3.

Find which cylinder has the greater volume. Volume of Cylinders Find which cylinder has the greater volume. Cylinder 1: V = r2h V  3.14  1.52  12 V  84.78 cm3 Cylinder 2: V = r2h V  3.14  32  6 V  169.56 cm3 Cylinder 2 has the greater volume because 169.56 cm3 > 84.78 cm3.