Calculating Volume and Surface Area of a Cone

This video tutorial covers the concepts of surface area and volume, focusing on cones. It explains the dimensions of a cone, including height, radius, and slant height, and provides formulas for calculating surface area and volume. The tutorial includes example calculations and demonstrates how to solve for missing dimensions using the given formulas.

What is the term used to describe the vertical distance from the tip of the cone to the base?

• Circumference

• Height

• Radius

• Slant height

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

• s = sqrt(r^2 + h^2)

• s^2 = r^2 + h^2

• s = r + h

• s^2 = r^2 - h^2

Which formula represents the area of the circular base of a cone?

• 2 * pi * r

• pi * r^2

• pi * r * s

• 1/3 * pi * r^2 * h

How do you calculate the lateral surface area of a cone?

• pi * r^2

• pi * r * s

• pi * (r^2 + s^2)

• pi * r * (r + s)

What fraction of the cylinder's volume is the volume of a cone with the same base and height?

• 1/2

• 1/4

• 3/4

• 1/3

What is the formula to find the volume of a cone?

• 1/3 * pi * r^2 * h

• pi * r^2 * h

• pi * r * h

• 1/2 * pi * r^2 * h

If the radius of a cone is 3 units, what is the formula for the surface area of the cone?

• pi * 3 * (3 + s)

• pi * (9 + 3s)

• pi * 3^2 + pi * 3 * s

• 2 * pi * 3 * s

Given a cone's radius of 5 cm and a lateral surface area of 179 cm^2, what is the slant height?

• 28.6 cm

• 11.4 cm

• 17.9 cm

• 35.8 cm

If the slant height and radius of a cone are 11.4 cm and 5 cm respectively, what is the height of the cone?

• 10.4 cm

• 9.6 cm

• 4.96 cm

• 11.4 cm

How do you find the height of a cone if you know the slant height and the radius?

• sqrt(s^2 - r^2)

• sqrt(s^2 + r^2)

• s - r

• s + r