Find the volume of each cone. Round your answer to two decimal places. (Use 3.14 for [tex]$\pi$[/tex].)
Answer (2)
Calculate the volume of cone 4 using the expression V 4 = 3 1 × 3 × 167.46 , which equals 167.46 .
Calculate the volume of cone 6 using the expression V 6 = 3 1 × 3.14 × 19 × 6 × 6 , which equals 715.92 .
Calculate the volume of cone 7 using the expression V 7 = 3 1 × 3.14 × 15 × 3 × 381 , which equals 17945.10 .
State the final volumes for each cone, rounded to two decimal places: V 4 = 167.46 , V 6 = 715.92 , V 7 = 17945.10 .
Explanation
Problem Analysis The problem asks us to find the volume of three different cones, rounding each answer to two decimal places. We are given the expressions to calculate the volumes directly, using π = 3.14 . The formula for the volume of a cone is V = 3 1 π r 2 h , where r is the radius and h is the height.
Calculate Volume of Cone 4 For cone 4, the volume is given by the expression: V 4 = 3 1 × 3 × 167.46 Calculating this gives: V 4 = 167.46 Rounding to two decimal places, we get 167.46 .
Calculate Volume of Cone 6 For cone 6, the volume is given by the expression: V 6 = 3 1 × 3.14 × 19 × 6 × 6 Calculating this gives: V 6 = 715.92 Rounding to two decimal places, we get 715.92 .
Calculate Volume of Cone 7 For cone 7, the volume is given by the expression: V 7 = 3 1 × 3.14 × 15 × 3 × 381 Calculating this gives: V 7 = 17945.1 Rounding to two decimal places, we get 17945.10 .
Final Answer Therefore, the volumes of the cones, rounded to two decimal places, are: Cone 4: 167.46 Cone 6: 715.92 Cone 7: 17945.10
Examples
Cones are common shapes in everyday life, from ice cream cones to traffic cones. Understanding how to calculate their volume is useful in many practical situations. For example, if you're filling ice cream cones at a shop, you'd want to know the volume to ensure you don't overfill them. Similarly, knowing the volume of a traffic cone helps in calculating the amount of material needed to manufacture them. The formula V = 3 1 π r 2 h allows us to determine the space a cone occupies, which is essential for design, manufacturing, and even serving desserts!
To find the volume of cones, use the formula V = 3 1 π r 2 h with π ≈ 3.14 . Calculate volumes using the given radius and height for each cone, rounding answers to two decimal places. Make sure to adjust the specific values for radius and height according to the cones you are analyzing.
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