volume of prisms and cylinders

What is volume?

A prism is a three-dimensional figure named for the shape of its bases A prism is a three-dimensional figure named for the shape of its bases. The two bases are congruent polygons. All of the other faces are parallelograms. A cylinder has two circular bases.

If all six faces of a rectangular prism are squares, it is a cube. Remember! Triangular prism Rectangular prism Cylinder Height Height Height Base Base Base

VOLUME OF PRISMS AND CYLINDERS Words Numbers Formula Prism: The volume V of a prism is the area of the base B times the height h. Cylinder: The volume of a cylinder is the area of the base B times the height h. B = 2(5) = 10 units2 V = Bh V = 10(3) = 30 units3 B = p(22) V = Bh = 4p units2 = (pr2)h V = (4p)(6) = 24p  75.4 units3

Area is measured in square units. Volume is measured in cubic units. Helpful Hint

Additional Example 1A: Finding the Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. A. A rectangular prism with base 2 cm by 5 cm and height 3 cm. B = 2 • 5 = 10 cm2 Area of base V = Bh Volume of a prism = 10 • 3 = 30 cm3

Additional Example 1B: Finding the Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. B. B = p(42) = 16p in2 Area of base 4 in. V = Bh Volume of a cylinder 12 in. = 16p • 12 = 192p  602.9 in3

Additional Example 1C: Finding the Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. B = • 6 • 5 = 15 ft2 1 2 C. Area of base 5 ft V = Bh Volume of a prism = 15 • 7 = 105 ft3 7 ft 6 ft

Try This: Example 1A Find the volume of the figure to the nearest tenth. A. A rectangular prism with base 5 mm by 9 mm and height 6 mm. B = 5 • 9 = 45 mm2 Area of base V = Bh Volume of prism = 45 • 6 = 270 mm3

Try This: Example 1B Find the volume of the figure to the nearest tenth. B = p(82) Area of base B. 8 cm = 64p cm2 V = Bh Volume of a cylinder 15 cm = (64p)(15) = 960p  3,014.4 cm3

Try This: Example 1C Find the volume of the figure to the nearest tenth. C. B = • 12 • 10 1 2 Area of base 10 ft = 60 ft2 V = Bh Volume of a prism 14 ft = 60(14) = 840 ft3 12 ft

Lesson Quiz Find the volume of each figure to the nearest tenth. Use 3.14 for p. 10 in. 1. 2. 3. 2 in. 12 in. 12 in. 10.7 in. 15 in. 3 in. 8.5 in. 942 in3 306 in3 160.5 in3