MCAS 2000, 10th Grade Math, Questions 13-16

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Question #13 (Open-Response Question)

Use the cone and sphere below to answer question 13.

a. If the height of the cone is doubled, the volume of the cone is how many times larger?

b. If the radius of the cone is doubled, the volume of the cone is how many times larger?

c. If the radius of the sphere is doubled, the volume of the sphere is how many times larger?

d. A manufacturing company wants to make one cone-shaped container and one sphere-shaped container that each have the same radius and the same volume. What must be the height of the cone in terms of its radius? Explain your reasoning.

Question #14 (Short-Answer Question)

You may want to use the following grid to help you answer question 14.

What are the coordinates of the midpoint of a line segment with endpoints (-3,-1) and (5,3)?

Question #15 (Short-Answer Question)

Use the figure below to answer question 15.

Ms. Barnes is building a railing for her stairs. The board along the side of the stairs, the railing, and the posts form parallelograms. If angle EDA shown in the figure measures 120o, what is the measure of angle ABC?

Question #16 (Open-Response Question)

A 15-player tournament consists of a series of matches between two contestants. A contestant is eliminated after losing one match. When there is an odd number of players, one player is not paired with a partner and automatically advances to the next round as though he/she had won a match.

a. Draw a diagram to show how the tournament could be set up.

b. What is the smallest number of two-contestant matches that the winner must play in order to become the champion?

c. What is the total number of matches that must be played in the tournament to determine a winner?

d. Suppose 63 people entered a similar tournament. What is the total number of matches that must be played in the tournament to determine a winner?

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