Volume Standards Review for NYS Geometry

The video tutorial covers key concepts of volume and density, providing strategies for solving related problems. It emphasizes the importance of writing formulas, drawing diagrams, and labeling. The tutorial explains how to rotate 2D shapes into 3D objects and solve problems involving hemispherical tanks, pyramids, and truncated cones. Each section provides step-by-step guidance on using the appropriate formulas and calculations to find volumes.

What is the first step you should take when solving a volume or density problem?

• Write down the formula

• Draw a diagram

• Label the numbers

• Guess the answer

When rotating a right triangle, what three-dimensional shape is formed?

• Cone

• Sphere

• Cylinder

• Pyramid

What is the formula for the volume of a sphere?

• πr^2h

• 2/3 πr^3

• 1/3 πr^2h

• 4/3 πr^3

If the diameter of a hemispherical tank is 10 feet, what is the radius?

• 5 feet

• 15 feet

• 2.5 feet

• 10 feet

What additional step must be taken when calculating the volume of a hemisphere?

• Divide by 2

• Multiply by 2

• Subtract the diameter

• Add the radius

What is the formula for the volume of a pyramid?

• 1/3 πr^2h

• 1/3 Bh

• 1/2 Bh

• Bh

If the volume of a pyramid is given and the height is known, what must be done to find the side length of the square base?

• Divide the volume by the height

• Take the square root of the base area

• Subtract the height from the volume

• Multiply the volume by the height

What is the shape of the base of a regular pyramid?

• Rectangle

• Triangle

• Circle

• Square

What is the formula for the volume of a cone?

• 1/3 πr^2h

• πr^2h

• 1/2 πr^2h

• 4/3 πr^3

When dealing with a truncated cone, what must be done to find the volume?

• Add the volumes of the two cones

• Divide the volume of the larger cone by the smaller cone

• Subtract the volume of the smaller cone from the larger cone

• Multiply the volumes of the two cones