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Volume and Surface Area of Cone

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Questions and Answers

What is the relationship between the slant height, radius, and height of a cone?

The slant height is always greater than the height of the cone.

The slant height is always equal to the hypotenuse of a right-angled triangle with base and height as its other two sides. (correct)

The slant height is always equal to the radius of the cone.

The slant height is always equal to the sum of the radius and height of the cone.

What is the formula for the volume of a cone?

$rac{1}{3} imes ext{base area} imes ext{height}$ (correct)

$rac{1}{3} imes ext{base area} imes ext{slant height}$

$rac{1}{3} imes ext{base circumference} imes ext{height}$

$rac{1}{3} imes ext{base circumference} imes ext{slant height}$

How does changing the radius of a cone affect its surface area?

The surface area decreases as the radius increases.

The surface area remains constant regardless of the radius.

The surface area increases as the radius increases. (correct)

The surface area is inversely proportional to the square of the radius.

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

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Description

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.