# Volume and angle of a cone

Please help with the attached problem.

Shown at the right is a cone with a slant height of 10 cm. Let's explore the relationship between the volume and the angle at the top of the cone....

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#### Solution Summary

This is a series of questions that help explore the relationship between the volume of a cone and the angle formed at the top with the slant height constant.

Geometry Supplementary Angles

1. Use the figure below to find the following:

[Please refer to the attachment for the figure and problem details]

2. Angle PQR and Angle ABC are supplementary angles and Angle PQR is nine times as large as Angle ABC. Determine the measure of each angle.

3. What is the exact area of a circle with a diameter of 11 inches?

4. The following triangles, Angle ABC and Angle DEF, are congruent.

[Please refer to the attachment for the figure]

Find the lengths of all missing sides and measures of all angles for both triangles. Include correct units with each of your answers.

First triangle: Second triangle:

Side AB = Side DF =

Angle BAC = Side EF =

Angle ABC =

Angle DEF =

Angle EFD =

5. Find the area of a trapezoid with a height of 4 m and bases of 13 m and 22 m.

6. A recreation room has the following dimensions. Carpeting will cost $1.50 a square foot. How many square feet of carpet will be needed and how much will it cost? Include correct units at each stage within your solution.

7. Find the perimeter and area of a right triangle if the shortest side is 20 mm. and the longest side is 52 mm. Include correct units with each part of your solution

8. How many cubic centimeters can a cigar box hold if its dimensions are 4 centimeters by 13 centimeters by 8 centimeters? Include correct units with your solution.

9. An ice cube that measures 2.4 centimeters on each side contains how many cubic centimeters of ice? Include correct units with your solution.

10. Find the approximate value of the volume of the right circular cone with a circular base shown below. Approximate your solution to the nearest hundredth.

[Please refer to the attachment for the figure]

11. In a 9 inch square cake pan and a 10 inch square cake pan, what is the difference in volume each pan will hold? Assume each pan is 2 inches high. Show step by step work. Include correct units with your solution.

12. For the following floor plan, determine whether it is possible for a person to walk through each doorway without using any of the doorways twice. If it is possible, state such a path. If it is not possible, answer, "not possible."

[Please refer to the attachment for the figure]

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