Volume and Area Formulas

The video tutorial explains the concept of volume, focusing on right solids and cylinders. It introduces the formula for volume as the area of the base times the height and demonstrates how to calculate the volume of different shapes, including a right solid with a rectangular and semicircular base, and a right circular cylinder. The tutorial also covers simplified calculations when the area of the base is provided.

What is the formula for the volume of a right solid?

• Perimeter of the base times the height

• Area of the base times the height

• Area of the base plus the height

• Perimeter of the base plus the height

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CCSS.7.G.A.3

Which two shapes make up the base in the example discussed?

• Rectangle and triangle

• Square and semicircle

• Rectangle and semicircle

• Circle and triangle

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CCSS.7.G.B.4

How do you calculate the area of a semicircle?

• Half of pi times radius squared

• Pi times radius squared

• Pi times diameter

• Half of pi times diameter

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CCSS.7.EE.A.1

What is the result of distributing 10 over the expression (40 + 2π)?

• 400 + 2π

• 40 + 2π

• 40 + 20π

• 400 + 20π

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CCSS.7.G.A.3

What is the base shape of the right circular cylinder discussed?

• Rectangle

• Square

• Triangle

• Circle

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CCSS.7.G.B.4

What is the formula for the area of a circle?

• 2πr

• πr²

• πd

• 2πr²

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the volume of a cylinder with a base area of 36π and height of 20?

• 360

• 720

• 360π

• 720π

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CCSS.7.G.B.6

If the area of the base is given as 50 cm² and the height is 12 cm, what is the volume?

• 600 cm³

• 700 cm³

• 800 cm³

• 500 cm³

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the advantage of having the area of the base already provided?

• It requires additional steps

• It simplifies the volume calculation

• It changes the formula used

• It allows for more complex calculations

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CCSS.5.MD.C.3A

CCSS.5.MD.C.3B

CCSS.5.MD.C.4

What is the unit of volume for a 3D object?

• Square units

• Cubic units

• Linear units

• Circular units

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CCSS.5.MD.C.3B

CCSS.5.MD.C.4

CCSS.5.MD.C.3A