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.

b.) c.) d.) a.)

Parts of a ConeCone- 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.

Activity 1 Surface Area of a Right ConeThe surface area of a right cone can be found by

adding the area of the base and lateral surface together.

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

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Note Card7.5.1 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= l + r^2𝝅 𝝅

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 r^2 h𝝅

Finding VolumeHaley 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.

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Example 2A 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?

Homework

7.5 Worksheet

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