Exploring Surface Area and Volume of a Cone

This video tutorial explains how to calculate the surface area and volume of a cone. It begins with an introduction to cones, comparing them to pyramids, and then details the formulas for lateral area, surface area, and volume. The tutorial includes two example calculations, demonstrating how to apply these formulas using given dimensions and the Pythagorean theorem.

What shape is the base of a cone?

• Square

• Triangle

• Circle

• Rectangle

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

• πr^2

• πrl

• πr(h + l)

• 2πrh

How is the surface area of a cone calculated?

• 2πr(h + l)

• πr^2h

• πr^2 + πrl

• Lateral area + area of the base

What is the volume formula for a cone?

• 1/3πr^2h

• πr^2h

• 2/3πr^2h

• πr^2 + h

How do you find the slant height of a cone?

• Using the circumference of the base

• Applying the Pythagorean theorem

• Multiplying the radius by π

• Adding the radius to the height

What is the lateral area of a cone with a radius of 5 and a slant height of 13?

• 78π inches squared

• 40π inches squared

• 25π inches squared

• 65π inches squared

What is the surface area of a cone with a base area of 25π and a lateral area of 65π?

• 40π inches squared

• 90π inches squared

• 100π inches squared

• 50π inches squared

What is the volume of a cone with a base area of 25π and a height of 12?

• 300π inches cubed

• 75π inches cubed

• 100π inches cubed

• 150π inches cubed

If the diameter of a cone is 10, what is the radius?

• 15

• 20

• 5

• 10

What is the volume of a cone with a base area of 25π and a height of 10.02?

• 75π kilometers cubed

• 100.2π kilometers cubed

• 250π kilometers cubed

• 83.5π kilometers cubed