Holt CA Course Volume of Prisms and Cylinders MG2.1 Use formulas routinely for finding the perimeter and area of basic two- dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Also covered: MG2.4 California Standards

Holt CA Course Volume of Prisms and Cylinders The volume of a three-dimensional figure is the number of cubes it can hold. Each cube represents a unit of measure called a cubic unit.

Holt CA Course Volume of Prisms and Cylinders Height Triangular prism Rectangular prism Cylinder Base Height Base Height Base

Holt CA Course Volume of Prisms and Cylinders

Holt CA Course Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. A. Additional Example 1: Finding the Volume of Prisms and Cylinders = 192 ft 3 B = 4 12 = 48 ft 2 V = Bh = 48 4 The base is a rectangle. Volume of a prism Substitute for B and h. Multiply.

Holt CA Course Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. Use 3.14 for . B. = 192 in 3 B = (4 2 ) = 16 in 2 V = Bh = 16 12 Additional Example 1: Finding the Volume of Prisms and Cylinders The base is a circle. Volume of a cylinder Substitute for B and h. Multiply.

Holt CA Course Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. Use 3.14 for . C. 7 ft V = Bh = 15 7 = 105 ft 3 B = 6 5 = 15 ft Additional Example 1: Finding the Volume of Prisms and Cylinders The base is a triangle. Volume of a prism Substitute for B and h. Multiply.

Holt CA Course Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. Use 3.14 for . A. = 180 in 3 B = 6 3 = 18 in. 2 V = Bh = The base is a rectangle. Volume of prism Check It Out! Example 1 Substitute for B and h. Multiply. 10 in. 6 in. 3 in.

Holt CA Course Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. Use 3.14 for . B. 8 cm 15 cm B = (8 2 ) = 64 cm 2 = (64)(15) = 960  3,014.4 cm 3 Check It Out! Example 1 The base is a circle. Volume of a cylinder V = Bh Substitute for B and h. Multiply.

Holt CA Course Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. C. 10 ft 14 ft 12 ft = 60 ft 2 = 60(14) = 840 ft 3 Check It Out! Example 1 The base is a triangle. Volume of a prism B = V = Bh Substitute for B and h. Multiply.

Holt CA Course Volume of Prisms and Cylinders A juice box measures 3 in. by 2 in. by 4 in. Explain whether tripling only the length, width, or height of the box would triple the amount of juice the box holds. Additional Example 2A: Exploring the Effects of Changing Dimensions The original box has a volume of 24 in 3. You could triple the volume to 72 in 3 by tripling any one of the dimensions. So tripling the length, width, or height would triple the amount of juice the box holds.

Holt CA Course Volume of Prisms and Cylinders A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling only the height of the can would have the same effect on the volume as tripling the radius. Additional Example 2B: Exploring the Effects of Changing Dimensions By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to 9 times the original volume.

Holt CA Course Volume of Prisms and Cylinders A box measures 5 in. by 3 in. by 7 in. Explain whether tripling only the length, width, or height of the box would triple the volume of the box. Check It Out! Example 2A Tripling the length would triple the volume. V = (15)(3)(7) = 315 cm 3 The original box has a volume of (5)(3)(7) = 105 cm 3.

Holt CA Course Volume of Prisms and Cylinders Check It Out! Example 2A Continued The original box has a volume of (5)(3)(7) = 105 cm 3. Tripling the height would triple the volume. V = (5)(3)(21) = 315 cm 3

Holt CA Course Volume of Prisms and Cylinders Check It Out! Example 2A Continued Tripling the width would triple the volume. V = (5)(9)(7) = 315 cm 3 The original box has a volume of (5)(3)(7) = 105 cm 3.

Holt CA Course Volume of Prisms and Cylinders By tripling the radius, you would increase the volume nine times. A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling only the radius or height of the cylinder would triple the amount of volume. Check It Out! Example 2B V = 36 3 = 108 cm 3 The original cylinder has a volume of 4 3 = 12 cm 3.

Holt CA Course Volume of Prisms and Cylinders Check It Out! Example 2B Continued Tripling the height would triple the volume. V = 4 9 = 36 cm 3 The original cylinder has a volume of 4 3 = 12 cm 3.

Holt CA Course Volume of Prisms and Cylinders A drum company advertises a snare drum that is 4 inches high and 12 inches in diameter. Estimate the volume of the drum. Additional Example 3: Music Application d = 12, h = 4 r = = = 6 Volume of a cylinder d2d2 V = (r 2 )h 12 2 = (3.14)(6) 2 4 = (3.14)(36)(4) = ≈ 452 Use 3.14 for . The volume of the drum is approximately 452 in 3.

Holt CA Course Volume of Prisms and Cylinders A drum company advertises a bass drum that is 12 inches high and 28 inches in diameter. Estimate the volume of the drum. Check It Out! Example 3 d = 28, h = 12 r = = = 14 Volume of a cylinder d2d2 V = (r 2 )h 28 2 = (3.14)(14) 2 12 = (3.14)(196)(12) = ≈ 7,385 Use 3.14 for . The volume of the drum is approximately 7,385 in 3.

Holt CA Course Volume of Prisms and Cylinders Find the volume of the the barn. Volume of barn Volume of rectangular prism Volume of triangular prism + = = 30, ,000 V = (40)(50)(15) + (40)(10)(50) 1212 = 40,000 ft 3 The volume of the barn is 40,000 ft 3. Additional Example 4: Finding the Volume of Composite Figures

Holt CA Course Volume of Prisms and Cylinders Check It Out! Example 4 Find the volume of the play house. 3 ft 4 ft 8 ft 5 ft V = (8)(3)(4) + (5)(8)(3) 1212 = V = 156 ft 3 Volume of house Volume of rectangular prism Volume of triangular prism + = The volume of the play house is 156 ft 3.