Exploring Adding and Subtracting Rational Expressions

This video tutorial covers the concepts of volume and surface area for spheres and hemispheres. It begins with an introduction to the properties of spheres, including diameter, radius, and great circles. The video then explains how to calculate the volume and surface area of spheres, followed by similar calculations for hemispheres. Several examples are provided to illustrate these calculations. The tutorial concludes with application problems that demonstrate how to use these formulas in real-world scenarios.

What is the name of the circle that divides a sphere into two hemispheres?

• Equator

• Great circle

• Meridian

• Equilateral circle

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CCSS.HSG.C.A.2

What formula is used to calculate the volume of a sphere?

• 4πr²

• 4/3 πr³

• 2/3 πr³

• πr²h

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

If the diameter of a sphere is 33, what is its radius?

• 16.5

• 33

• 8.25

• 66

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CCSS.7.G.B.4

What is the formula for the surface area of a sphere?

• 4πr²

• 2πr²

• 2/3πr²

• πr²

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

For a sphere with a radius of 12, what is its surface area?

• 452.16π

• 576π

• 1728π

• 144π

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What adjustment is made to the sphere's volume formula to calculate the volume of a hemisphere?

• Multiply by 2/3

• Multiply by 1/2

• Divide by 2

• Divide by 3

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

If a hemisphere has a radius of 9, what is its volume?

• 243π

• 486π

• 729π

• 1526.8

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How do you find the radius from the great circle's area?

• Square root of (area/π)

• π times the square root of area

• Area divided by π

• Area times π

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CCSS.7.G.B.4

What is the combined volume of a hemisphere and a cylinder if the hemisphere's radius is 11 and the cylinder's height is 34?

• 15712.15 cubic feet

• 2662π/3 + 4114π cubic feet

• 8436 cubic feet

• 4114π cubic feet

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CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

To find the surface area of a combined figure of a cone and a hemisphere, you need to subtract the area of which part?

• The base of the cone

• The great circle

• The hemisphere's curved surface

• The slant height