Calculating the Volume of a Hemisphere

The video tutorial explains the concept of a hemisphere as a three-dimensional figure that is half a sphere. It derives the formula for calculating the volume of a hemisphere by using the known formula for the volume of a sphere. The tutorial demonstrates the derivation process, simplifying the equation to two-thirds pi times the radius cubed. It then tests the derived formula with an example, confirming its accuracy by comparing it to the volume of half a sphere with the same dimensions.

What shape is half of a sphere known as?

• Cylinder

• Hemisphere

• Cube

• Cone

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CCSS.1.G.A.1

CCSS.2.G.A.1

What is the volume of a hemisphere related to a sphere with the same dimensions?

• Equal to the sphere's volume

• Twice the sphere's volume

• One fourth the sphere's volume

• Half the sphere's volume

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How do you calculate the volume of a sphere?

• 2/3 * π * radius^3

• 4/3 * π * radius^3

• π * radius^3

• π * radius^2

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the simplified formula for the volume of a hemisphere?

• 4/3 * π * radius^2

• 1/2 * π * radius^3

• π * radius^2

• 2/3 * π * radius^3

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What operation simplifies 4/6 to its lowest terms?

• Subtraction of 2

• Addition of 2

• Division by 2

• Multiplication by 2

What mathematical constant is used in the formula for the volume of a hemisphere?

• k

• e

• g

• π

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the first step in deriving the volume of a hemisphere?

• Cube the radius

• Simplify the fraction

• Multiply the sphere's volume by 2

• Divide the sphere's volume by 2

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

If a sphere's volume is 113.4 cubic centimeters, what is the volume of the corresponding hemisphere?

• 56.52 cubic centimeters

• 113.4 cubic centimeters

• 226.8 cubic centimeters

• 56.7 cubic centimeters

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the result of cubing the radius 3?

• 81

• 27

• 6

• 9

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CCSS.5.MD.C.5B

CCSS.6.G.A.2

How do you verify the accuracy of the hemisphere volume formula?

• Compare it to the volume of a cube

• Calculate and compare with half the sphere's volume

• Use it to calculate a known sphere's volume

• Apply it to a real-world object

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CCSS.5.MD.C.5C