Geometry: Surface Area and Volume of Cones and Spheres

What is the formula for the surface area of a cone?

What is the relationship between the volume of a cone and a cylinder with the same base radius and height?

What is the formula for the volume of a sphere?

Which expression correctly represents the total surface area of a cone?

What is the surface area formula for a sphere with radius 'r'?

Cone

Surface Area: The surface area of a cone comprises the area of the base and the lateral surface area.
Base Area: A circle with radius 'r'. Area = πr²
Lateral Surface Area: Calculated using the slant height 'l' and the radius 'r'. Area = πrl
Total Surface Area: The sum of the base area and lateral surface area. Total Surface Area = πr² + πrl
Formula: SA = πr(l+r)

Sphere

Surface Area: The entire exterior area of a sphere.
Formula: The surface area of a sphere with radius 'r' is given by 4πr².
Calculation: SA = 4πr²

Cone – Volume

Volume: The amount of space enclosed within a cone.
Formula: The volume of a cone with radius 'r' and height 'h' is given by (1/3)πr²h.
Relationship to Cylinder: A cone's volume is one-third the volume of a cylinder with the same base radius and height.
Calculation: V = (1/3)πr²h

Sphere – Volume

Volume: The amount of space enclosed within a sphere.
Formula: The volume of a sphere with radius 'r' is given by (4/3)πr³.

This quiz covers the formulas for calculating the surface area and volume of cones and spheres. It focuses on the relationships between the dimensions and the derived formulas necessary for solving related problems. Test your knowledge of geometry and solid figures with this quiz!