Exploring Volume Calculations for 3D Shapes

What is the primary skill practiced when calculating volumes as described in the video?

• Solving for variables

• Memorization of formulas

• Substitution of values into equations

• Drawing geometric figures

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CCSS.5.MD.C.5B

CCSS.6.G.A.2

Why is it unnecessary to memorize the volume formulas according to the video?

• Because they are provided during tests

• Because they are intuitive

• Because they are rarely used

• Because they can be easily derived

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CCSS.8.G.C.9

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What is the formula for the volume of a cone?

• V = 2πrh

• V = 4/3 πr^3

• V = πr^2h

• V = 1/3 πr^2h

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the volume of a cone with a radius of 3 cm and height of 13 cm, using π as 3.14?

• Approximately 122.46 cm^3

• Approximately 39 cm^3

• Approximately 1224.6 cm^3

• Approximately 392 cm^3

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CCSS.8.G.C.9

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What is the significance of the area of a circle in calculating the volume of a cone?

• It is used to calculate the slant height

• It is used to calculate the base area

• It is irrelevant to the volume

• It is used to calculate the height

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CCSS.8.G.C.9

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How do you find the volume of a cylinder?

• V = πr^2h

• V = 1/3 πr^2h

• V = 4/3 πr^3

• V = 2πrh

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the volume of a cylinder with a radius of 12 cm and height of 28 cm, using π as 3.14?

• Approximately 4320 cm^3

• Approximately 1266.4 cm^3

• Approximately 432 cm^3

• Approximately 12664 cm^3

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CCSS.8.G.C.9

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What is the formula for the volume of a sphere?

• V = 1/3 πr^2h

• V = πr^2h

• V = 4/3 πr^3

• V = 2πrh

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the volume of a sphere with a radius of 6 m, using π as 3.14?

• Approximately 9043.2 m^3

• Approximately 94.32 m^3

• Approximately 288 m^3

• Approximately 904.32 m^3

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What does the radius of a sphere represent?

• The surface area of the sphere

• The circumference of the sphere

• The diameter of the sphere

• The distance from the center to any point on the surface