A spherical basketball is packed in a cubical box into which it fits exactly. What percent of the volume of the box is used up by the basketball?

## Set 04

## Impossible Rectangle

Is it possible for a rectangle with a 48 cm perimeter to have an area of 150 square cm? Explain.

## Find Altitude, Given Sides

In triangle ABC, *a* = 7, *b* = 8, and *c* = 9. Find the altitude of the triangle to side *c*.

## Basketball Bounces

Levy Witherspoon is the star center of the boys’ varsity basketball team. If he drops the ball, it will bounce back to 8/10 of the height that he dropped it from. Levy reaches overhead and drops the ball from a height of eight feet. How many times will it bounce before it bounces up less than two feet (approximately the height of Levy’s knees)?

## Trapezoid Formed By Lines

The *x*-axis and the three lines *x* = 1, *x* = 4 and *y* = *mx* + 4 form a trapezoid. If the area of the trapezoid is 7, then what is *m*?

- -1/2
- -2/3
- -3/2
- -2
- none of these

## Circle & Triangle

The end points of a diameter of a circle are (3, 9) and (11, 3). A triangle inscribed in this circle has two of its vertices at the given points. Find the coordinates of all points at which a third vertex of the triangle can be located for this triangle to have its maximum possible area.

## Find Adjacent Corner of Square

The area of a square is 81. One corner of the square is at the point (5, -4). Which of these points could be an adjacent corner of the square?

- (5 – 6√2, 1)
- (-8, 6√2 – 4)
- (2, 6√2 – 4)
- (6√2 – 5, -1)
- (8, 4-6√2)

## Defined Operation; Do Inverse

Suppose a linear operation �/� is defined so that:

5 / = 11;

8 / = 17;

12 / = 25.

What is *n* if *n* / = 35?

## Complicated Ages (Andrea, Bonnie)

Andrea and Bonnie are comparing their ages; they find that Bonnie is as old as Andrea was when Bonnie was as old as Andrea had been when Bonnie had been half as old as Andrea is now. If the sum of their present ages is 44 years, then what is Andrea’s age?

## Backlot Books

Backlot Books sells used books. The store bought Henry’s collection of old Farm and Home magazines for $195.00. They sold the lot for $322.50, and this gave them a profit of 50 cents per magazine. How many magazines did Henry sell them?