Preview Warm Up California Standards Lesson Presentation

Warm Up 1. Find the volume of a rectangular prism that is 4 in. tall, 16 in. wide, and 48 in deep. 2. A cylinder has a height of 4.2 m and a diameter of 0.6 m. To the nearest tenth of a cubic meter, what is the volume of the cylinder? Use 3.14 for . 3. A triangular prism’s base is an equilateral triangle. The sides of the triangle are 4 ft, and the height of the prism is 8 ft. To the nearest cubic foot, what is the volume of the prism? 3072 in3 1.2 m3 55.4 ft3

Extension of 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. California Standards

The height of a pyramid or cone is measured from the highest point to the base along a perpendicular line.

Additional Example 1: Finding the Volume of Pyramids and Cones Find the volume of the figure. A. B = (4 • 7) = 14 cm2 1 2 1 3 V = • 14 • 6 V = Bh 1 3 V = 28 cm3

Additional Example 1: Finding the Volume of Pyramids and Cones Find the volume of the figure. Use 3.14 for p. B. B = (32) = 9 in2 1 3 V = • 9 • 10 V = Bh 1 3 V = 30  94.2 in3 Use 3.14 for .

Check It Out! Example 1 Find the volume of the figure. A. B = (5 • 7) = 17.5 in2 1 2 7 in. 1 3 V = • 17.5 • 7 V = Bh 1 3 5 in. 7 in. V  40.8 in3

Check It Out! Example 1 Find the volume of the figure. Use 3.14 for p. B. B = (32) = 9 m2 7 m 1 3 V = • 9 • 7 V = Bh 1 3 3 m V = 21  65.9 m3 Use 3.14 for .

Additional Example 2: Social Studies Application The Pyramid of Kukulcán in Mexico is a square pyramid. Its height is 24 m and its base has 55 m sides. Find the volume of the pyramid. Step 1: Find the area of the base. B = 552 The base is a square. = 3025 m2 Multiply.

Additional Example 2 Continued The Pyramid of Kukulcán in Mexico is a square pyramid. Its height is 24 m and its base has 55 m sides. Find the volume of the pyramid. Step 2: Find the volume. 1 3 V = Bh Write the formula. 1 3 V = (3025)(24) Substitute for B and h. V = 24,200 m3 Multiply. The volume of the pyramid is 24,200 m3.

Check It Out! Example 2 Find the volume of a pyramid with a height of 12 m and a base with 48 m sides. Step 1: Find the area of the base. B = 482 The base is a square. = 2304 m2 Multiply.

Check It Out! Example 2 Continued Find the volume of a pyramid with a height of 12 m and a base with 48 m sides. Step 2: Find the volume. 1 3 V = Bh Write the formula. 1 3 V = (2304)(12) Substitute for B and h. V ≈ 9216 m3 Multiply. The volume of the pyramid is 9,216 m3.

Lesson Quiz: Part l Find the volume of each figure to the nearest tenth. Use 3.14 for p. 1. the triangular pyramid 6.3 m3 2. the cone 78.5 in3

Lesson Quiz: Part ll 3. Explain whether tripling the height of the triangular pyramid would triple the volume. Yes; the volume is one-third the product of the base area and the height. So if you triple the height, the product would be tripled.