Volume of Cones, Day 2. Warm Up A party favor is made by joining two cones to the bases of a cylinder. The cylinder is 6 centimeters long and has a diameter.

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Presentation transcript:

Volume of Cones, Day 2

Warm Up

A party favor is made by joining two cones to the bases of a cylinder. The cylinder is 6 centimeters long and has a diameter of 4 centimeters. Each cone has a height of 3 centimeters. Find the volume of the party favor to the nearest tenth.

How do you find the volume of a cone? Find one- third of the product of the area of the circular base and the height of the cone. Some may try to measure the height of a cone from the vertex to a point on the circumference of the base, which is the slant height. The height is a segment perpendicular to the base from the vertex to the center of the circular base. Compare and contrast a cone and a pyramid. A cone has one circular base and a curved lateral surface; a pyramid has one base that is a polygon and sides that are triangles. Compare and contrast a cone and a cylinder. A cone has one circular base and a curved lateral surface; a cylinder has two congruent circular bases and a curved lateral surface.

A cone has two aspects that are referred to as height. The height of the cone is the length of the segment from the vertex perpendicular to the center of the base. For a right circular cone, this height joins the vertex and the center of the base. The slant height is the length of the segment from the vertex to any point on the circumference of the circular base. The slant height is used to find the lateral surface area of a cone.

What step is similar when you find the volume of a cone, a cylinder, or a prism? You have to find the area of the base and multiply by the height. What do you think is the most important difference between a cone and a cylinder or prism when you need to find the volume? The volume for a cone is one-third of the product of the base area and height.

A styrofoam model of a volcano is in the shape of a cone. The model has a circular base with a diameter of 48 centimeters and a height of 12 centimeters. Find the volume of foam in the model to the nearest tenth. Use 3.14 for ∏.

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