Geometry and Volume Problems

This video tutorial covers various mathematical problems related to cone dimensions, including calculating the volume of a cone from a cylinder, finding the radius of a cone given its volume and height, and determining the height of a cone for different radii. It also includes graph interpretation exercises and a problem on window placement in a room, emphasizing the relationship between different variables.

If a cylinder and a cone have the same base area and height, how does the volume of the cylinder compare to the cone?

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

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

• The cylinder's volume is twice the cone's volume.

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

Given a cone with a volume of 12π cubic inches and a height of 4 inches, what is the radius?

• 3 inches

• 5 inches

• 2 inches

• 4 inches

What is the height of a cone with a volume of 3π cubic inches and a radius of 1?

• 6 units

• 12 units

• 3 units

• 9 units

If a cone's radius is 2, what is its height given the volume is 3π cubic inches?

• 2.25 units

• 1 unit

• 3.5 units

• 4.5 units

For a cone with a radius of 5, what is the height if the volume is 3π cubic inches?

• 0.72 units

• 0.45 units

• 0.9 units

• 0.36 units

In the zipline problem, which graph represents the person standing on the dock?

• An ascending line from 0 feet

• A descending line from 20 feet

• A horizontal line at 10 feet

• A horizontal line at 5 feet

Which graph represents the person ziplining into the water?

• A horizontal line at 10 feet

• A horizontal line at 5 feet

• A descending line from 20 feet

• An ascending line from 0 feet

In the window placement problem, what is the independent variable?

• The distance from the ceiling to the window

• The distance from the floor to the window

• The height of the window

• The height of the room

If the distance from the floor to the window is 3 feet, what is the distance from the ceiling to the window?

• 7 feet

• 6 feet

• 8 feet

• 5 feet

If the customer wants 5 feet of space above the window, what is the distance from the floor to the window?

• 3 feet

• 4 feet

• 5 feet

• 6 feet