3 Questions
What is the relationship between the slant height, radius, and height of a cone?
The slant height is always equal to the hypotenuse of a right-angled triangle with base and height as its other two sides.
What is the formula for the volume of a cone?
$rac{1}{3} imes ext{base area} imes ext{height}$
How does changing the radius of a cone affect its surface area?
The surface area increases as the radius increases.
Study Notes
Properties of a Cone
- The slant height, radius, and height of a cone are related by the Pythagorean theorem: slant height² = radius² + height²
- The slant height is the distance from the center of the base to the apex of the cone
Volume of a Cone
- The formula for the volume of a cone is (1/3)πr²h, where r is the radius and h is the height
- The volume of a cone is one-third the area of the base (πr²) multiplied by the height (h)
Surface Area of a Cone
- The surface area of a cone is affected by the radius: increasing the radius increases the surface area
- The surface area of a cone is the sum of the area of the base (πr²) and the lateral surface area (πrl, where l is the slant height)
- Changing the radius affects the lateral surface area, which in turn affects the overall surface area of the cone
Test your knowledge on the formulas for calculating the volume and surface area of a cone, as well as the relationship between the slant height, radius, and height of a cone. Explore how changes in the radius of a cone impact its surface area.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
