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Warm-ups

Warm-ups. Warm up #1: Find the circumference and the area of a circle with a radius of 10. K eep in pie form. Warm up #2: Which one of these figures are examples of a cone? Explain your answer. a.). b.). c.). d.). Parts of a Cone.

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Warm-ups

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  1. Warm-ups Warm up #1: Find the circumference and the area of a circle with a radius of 10. Keep in pie form. Warm up #2: Which one of these figures are examples of a cone? Explain your answer. a.) b.) c.) d.)

  2. Parts of a Cone Cone- A three-dimensional figure that consists of a circular base and a curved lateral surface that connects the base to the vertex. Vertex-Single point not in the plane of the base. Altitude of a Cone-The Perpendicular segment from the vertex to the plane of the base. Height of a Cone-The length of the altitude. Slant Height of a Cone-The distance from the top, down the side, to a point on the base circumference. Right Cone-If the altitude of a cone intersects the base of the cone at its center, the cone is a right cone. Oblique Cone-If the altitude of a cone does not intersect the base of the cone at its center, the cone is a oblique cone.

  3. Activity 1 Surface Area of a Right Cone The surface area of a right cone can be found by adding the area of the base and lateral surface together. 3

  4. Example 1 Find the surface area of a right cone with the indicated measurements. 7 15

  5. Note Card 7.5.1 Surface Area of a Right Cone The surface area, S, of a right cone with lateral area L, base of area B, radius r, and slant height l is S = L + B   or   S=𝝅 l + 𝝅 r^2 7.5.2 Volume of a Cone The volume, V, of a cone with radius r, or height h, and base area B is V = 1/3 BH   or   V = 1/3 𝝅 r^2 h

  6. Finding Volume Haley wanted to find out the exact volume inside the cone with the dimensions of h= 10 r= 3. Find the volume, round to the nearest tenths if necessary. 10 3

  7. Example 2 A volcanologist is studying a violent eruption of a cone-shaped volcano. The original volcanic cone had a radius of 5 miles and a height of 2 miles. The eruption removed a cone-shaped area from the top of the volcano. This cone had a radius of 1 mile and a height of ½ mile. What percent of the total volume of the original volcano was removed by the eruption?

  8. Homework 7.5 Worksheet # 1-10 odds

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