Finding surface area and volumes of cones Cone

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Finding surface area and volumes of cones

Finding surface area and volumes of cones

Cone • A cone is a 3 -dimensional figure with a circular base and

Cone • A cone is a 3 -dimensional figure with a circular base and a curved lateral surface that connects the base to a point called the vertex

• The circular face of a cone is the base of the cone.

• The circular face of a cone is the base of the cone. • The vertex of a cone is the point opposite the base. • The altitude of a cone is the perpendicular segment from the vertex to the plane containing the base. • If an altitude of a cone has an endpoint on the center of the base, then it is a right cone • If the altitude does not intersect the center of the base it is an oblique cone

• Slant height of a cone is the distance from the vertex of

• Slant height of a cone is the distance from the vertex of the cone to a point on the edge of the base. • The radius of a cone is the radius of the base of the cone.

Lateral surface area of a cone • Lateral surface area of a cone is

Lateral surface area of a cone • Lateral surface area of a cone is given by the following formula where r is the radius of the cone, and l is the slant height • L = rl

Finding lateral area of a cone • l=? • r=? • L=?

Finding lateral area of a cone • l=? • r=? • L=?

Calculate Lateral area of the cone to the nearest hundredth 13 in.

Calculate Lateral area of the cone to the nearest hundredth 13 in.

Surface area of a cone • The total surface area of a cone is

Surface area of a cone • The total surface area of a cone is given by the following formula, where L is the lateral area, and B is the area of the base • SA = L + B • Or • SA = rl + r 2

Calculating surface area of a cone • Calculate the surface area of a cone,

Calculating surface area of a cone • Calculate the surface area of a cone, in terms of pi, with a slant height of 9 cm. and a base radius of 5 cm. • L = 5(9) + B = (5)2 • SA = 45 + 25 • SA= 70 cm 2

Volume of a cone • The volume of a cone is given by the

Volume of a cone • The volume of a cone is given by the following formula, where B is the area of the base, and h is the altitude of the cone. • V = 1/3 Bh

Calculating volume of a cone • Find the volume of a cone with a

Calculating volume of a cone • Find the volume of a cone with a radius of 4 and a height of 7? • V = 1/3 Bh • V = 1/3 (3. 14)(16)(7)

Practice • A funnel used for extra-large family sized funnel cakes is a right

Practice • A funnel used for extra-large family sized funnel cakes is a right circular cone 7 inches tall with a radius of 3. 6 inches. How much batter can this funnel hold?

practice • 1. Calculate the area of a right cone with a radius of

practice • 1. Calculate the area of a right cone with a radius of 2 feet and a slant height of 7 feet. • 2. Calculate the total surface area of a cone with a height of 8 m. and a radius of 3 m. • 3. Calculate the volume of a right cone with a height of 10 in. and a radius of 6 inches. • 4. A traffic cone is about 70 cm. high and has a diameter of 20 cm. What is the volume of the cone.