Volume and Area of Cones

The video tutorial explains a word problem involving runners in a marathon receiving water in cone-shaped cups. It details how two-thirds of the water is lost when the runner grabs the cup, leaving only one-third to be consumed. The tutorial walks through the calculation of the remaining water volume using the formula for the volume of a cone, adjusting for the water lost. The final result is presented in terms of both pi and a numerical approximation.

What is the main issue faced by runners when they grab the water cups during the marathon?

• The water spills out due to the force of grabbing.

• The cups are difficult to open.

• The cups are too heavy to carry.

• The cups are not filled with enough water.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the formula for the volume of a cone?

• Volume = Base Area x Height x 3

• Volume = Base Area x Height / 2

• Volume = Base Area x Height

• Volume = Base Area x Height / 3

Tags

CCSS.4.NF.B.4B

CCSS.4.NF.B.4C

If two-thirds of the water spills out, what fraction of the original volume remains?

• One-fourth

• One-third

• One-half

• Two-thirds

Tags

CCSS.7.G.B.4

How do you calculate the area of the base of the cone?

• Using the formula pi x radius squared

• Using the formula pi x diameter

• Using the formula pi x radius cubed

• Using the formula 2 x pi x radius

What is the radius of the base of the cone in this problem?

• 5

• 2

• 4

• 3

Tags

CCSS.HSG.GMD.A.3

What is the next step after finding the area of the base in the volume calculation?

• Multiply by the height and divide by 3

• Multiply by the height and divide by 2

• Multiply by the height and divide by 5

• Multiply by the height and divide by 4

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the simplified volume of water left in terms of pi?

• 6 pi

• 7 pi

• 9 pi

• 8 pi

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

What is the numerical value of the remaining water volume using pi as 3.14?

• 27.12 cm³

• 24.12 cm³

• 25.12 cm³

• 26.12 cm³

Tags

CCSS.3.MD.A.2

What are the units of the final volume of water?

• Centimeters cubed

• Centimeters squared

• Centimeters

• Meters cubed

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Why might the numerical answer not appear on the homework?

• Because pi is not used in calculations

• Because pi is an approximation

• Because the volume is too small

• Because the units are incorrect

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3