Geometry and Volume Concepts

The video tutorial covers various geometry topics, including calculating the volume of cylinders and cubes, determining the scale factor of similar pyramids, and finding the volume of a new water storage tank. It also explains the cross-sections of a cone, the equation of a circle, and how to write equations for perpendicular and parallel lines. Additionally, the tutorial demonstrates using the midpoint formula to find a point between two others.

What is the formula for the volume of a cylinder?

• 2πr times height

• Base times height divided by 2

• Length times width times height

• Area of the base times height

If the diameter of a cylinder is 6 cm and the height is 4 cm, what is the volume in terms of π?

• 24π cubic cm

• 36π cubic cm

• 18π cubic cm

• 72π cubic cm

How do you find the scale factor of two similar pyramids with volumes 8 cubic feet and 343 cubic feet?

• Multiply the volumes together

• Divide the larger volume by the smaller volume

• Take the square root of each volume

• Take the cube root of each volume

What is the scale factor between two similar pyramids with volumes 8 cubic feet and 343 cubic feet?

• 2/7

• 7/2

• 3/4

• 4/3

Kendra increases the size of her compost box by extending each edge by half its original length. What is the percentage increase in volume?

• 200%

• 400%

• 337.5%

• 150%

A city's new water tank has a radius of 15 ft and the same height as the old tank with a radius of 12 ft. If the old tank's volume is 10,000 cubic feet, what is the new tank's volume?

• 15,625 cubic feet

• 20,000 cubic feet

• 18,000 cubic feet

• 22,500 cubic feet

What shape is formed when a plane passes through a cone parallel to its base?

• Square

• Circle

• Ellipse

• Triangle

What is the resulting shape when a plane passes through a cone perpendicular to its base?

• Circle

• Triangle

• Rectangle

• Ellipse

What is the technical term for an oval shape formed by a diagonal cross-section of a cone?

• Parabola

• Ellipse

• Hyperbola

• Circle

How do you find the center and radius of a circle from its equation?

• By using the distance formula

• By finding the midpoint

• By using the Pythagorean theorem

• By completing the square