Calculating Surface Area of Cones

The video tutorial covers the surface area of cones, explaining how to calculate it by considering both the circular base and the lateral surface area. It introduces the concept of slant height and demonstrates how to use the Pythagorean theorem to find it when necessary. The tutorial includes several example problems, ranging from simple to complex, to illustrate the calculation process. It also discusses how to handle cases where the diameter is given instead of the radius.

What does the lateral surface area of a cone include?

• The area around the cone excluding the base

• Only the top circle area

• Only the base area

• The total area including the inside of the cone

What happens to the circle's area in a composite surface area calculation when a cone is placed on top of a cylinder?

• It is doubled

• It is halved

• It is subtracted

• It remains the same

What is the term used for the diagonal height of a cone?

• Vertical height

• Slant height

• Diagonal line

• Cone length

How do you calculate the surface area of a cone when given the radius and slant height?

• Pi times radius squared plus pi times radius times slant height

• Pi times radius plus slant height

• Radius squared plus slant height squared

• Pi times radius times slant height squared

What theorem is used to find the slant height when only the height and radius are given?

• Euclidean theorem

• Pythagorean theorem

• Theorem of cones

• Slant height theorem

If the diameter of a cone is given as 20 units, what is the radius?

• 5 units

• 40 units

• 20 units

• 10 units

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

• Pi times radius squared plus pi times radius times height

• Pi times radius squared plus pi times radius times slant height

• Pi times diameter squared plus pi times diameter times slant height

• Pi times radius times height

In a right cone, if the height is 12 units and the radius is 5 units, what is the slant height?

• 7 units

• 17 units

• 12 units

• 13 units

How is the slant height calculated using the Pythagorean theorem?

• Square root of (radius squared plus height squared)

• Radius squared plus height squared

• Square root of (radius squared minus height squared)

• Height squared minus radius squared

When given the diameter of a cone, what must be done before calculating the surface area?

• Square the diameter

• Divide the diameter by 2 to find the radius

• Nothing, use the diameter as is

• Multiply the diameter by pi