Cone Volume and Properties

This video tutorial covers the concept of calculating the volume of a cone, comparing it to the volume of a cylinder, and exploring how changes in dimensions affect the volume. It includes practical examples and exercises to reinforce understanding, such as finding the volume of a cone with given dimensions and solving for the height of a cone when the volume is known.

What is the formula for the volume of a cone?

• 1/2 πr²h

• 1/3 πr²h

• πr²h

• 2/3 πr²h

If a cone has the same base but a height three times that of a cylinder, what is the relationship between their volumes?

• The cone's volume is half of the cylinder's volume.

• The cone's volume is one-third of the cylinder's volume.

• The cone's volume is three times the cylinder's volume.

• The cone's volume is equal to the cylinder's volume.

How does tripling the height of a cone affect its volume?

• The volume increases by a factor of nine.

• The volume doubles.

• The volume triples.

• The volume remains the same.

What happens to the volume of a cone if the radius is tripled?

• The volume doubles.

• The volume increases by a factor of nine.

• The volume remains the same.

• The volume triples.

What is the effect of increasing the radius of a cone on its volume?

• The volume decreases.

• The volume becomes zero.

• The volume remains constant.

• The volume increases.

Given a cone with a volume of 9,420 cubic mm and a radius of 30 mm, what is the height of the cone?

• 25 mm

• 20 mm

• 10 mm

• 15 mm

What is the first step in solving for the height of a cone given its volume and radius?

• Multiply the radius by the height.

• Use the formula 1/3 πr²h and solve for h.

• Divide the volume by the radius squared.

• Multiply the volume by π.

In the computation problem, what is the result of -3 - 13?

• -16

• 16

• 10

• -10

Which number has a greater absolute value: 31 or 13?

• 31

• 13

• Neither has an absolute value

• Both have the same absolute value

What is the result of dividing both sides of the equation -6x = 18 by -6?

• x = -6

• x = 6

• x = -3

• x = 3