Volume and Proportionality Concepts

This video tutorial covers various mathematical problems related to geometry and volume. It begins with estimating the volume of a baseball inside a cube, followed by exploring the volume of cones as a function of radius. The tutorial then calculates the volumes of a hemisphere, cylinder, and cone, and discusses finding diameters and radii of hemispheres. Finally, it models photo storage on a phone using a linear function.

If a baseball fits snugly inside a cube with an edge length of 2.9 inches, how does the volume of the baseball compare to the cube?

• The baseball's volume is twice the cube's volume.

• The baseball's volume is equal to the cube's volume.

• The baseball's volume is less than the cube's volume.

• The baseball's volume is greater than the cube's volume.

What is the equation for the volume of a cone with a height of 18 meters as a function of its radius?

• v = 12πr²

• v = 18πr²

• v = 6πr²

• v = 3πr²

If the radius of a cone is doubled, how does the volume change?

• The volume remains the same.

• The volume quadruples.

• The volume doubles.

• The volume triples.

What is the volume of a cylinder with a radius of 6 cm and height of 6 cm?

• 72π cm³

• 288π cm³

• 216π cm³

• 144π cm³

How do you estimate the volume of a hemisphere using the volumes of a cylinder and a cone?

• Subtract the volume of the cone from the cylinder.

• Add the volumes of the cylinder and cone, then divide by 3.

• Add the volumes of the cylinder and cone, then divide by 2.

• Multiply the volumes of the cylinder and cone.

If the radius of a hemisphere is 6 cm, what is its diameter?

• 3 cm

• 6 cm

• 12 cm

• 9 cm

What is the radius of a hemisphere if its diameter is 9.008 feet?

• 4.504 feet

• 9.008 feet

• 18.016 feet

• 3.004 feet

What is the constant of proportionality if the number of photos divided by memory used equals 3.2?

• 3.2

• 2.3

• 4.5

• 1.8

How many photos should Elena delete to free up 1200 megabytes of space?

• 375 photos

• 400 photos

• 350 photos

• 300 photos