Volume and Dimensions of Cones

This video tutorial explains how to find the volume of a cone when given the slant height and diameter. It begins by identifying the radius and using the Pythagorean theorem to calculate the height of the cone. The tutorial then demonstrates how to use these measurements to compute the volume using the formula for the volume of a cone. The process is broken down into clear steps, making it easy to follow and understand.

What is the diameter of the cone given in the problem?

• 15

• 12

• 9

• 6

Tags

CCSS.7.G.B.4

How do you calculate the radius of a cone if the diameter is known?

• Add 5 to the diameter

• Subtract 3 from the diameter

• Divide the diameter by 2

• Multiply the diameter by 2

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Which theorem is used to find the height of the cone?

• Pythagorean theorem

• Binomial theorem

• Fundamental theorem of calculus

• Fermat's Last theorem

Tags

CCSS.8.G.B.8

What is the value of the radius used in the Pythagorean theorem for this problem?

• 9

• 12

• 3

• 6

Tags

CCSS.8.G.B.8

What is the simplified form of the height calculated using the Pythagorean theorem?

• 3√5

• 9√5

• √45

• 5√3

What is the base area of the cone when the radius is 6?

• 12π

• 18π

• 36π

• 72π

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How is the volume of the cone calculated after finding the height?

• Base area times height

• Base area divided by height

• Base area plus height

• Base area minus height

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the final volume of the cone expressed in terms of π?

• 36√5π

• 72√5π

• 54√5π

• 108√5π

Tags

CCSS.5.MD.C.3A

CCSS.5.MD.C.3B

CCSS.5.MD.C.4

What units are used for the final volume of the cone?

• Linear units

• No units

• Cubic units

• Square units

What is the significance of the slant height in this problem?

• It is used to find the base area

• It is used to find the diameter

• It is used to find the height

• It is used to find the radius