Pinexam——There is royal road to learning.

## RST is a right triangle with side lengths of r, s, and t, as shown below. What is the value of cos2 S + cos2 R?

(F) 1

(G)

(H)

(J)

(K)

Explanation

The perimeter of an elliptical billiard table is to be covered with red velvet. The perimeter of an ellipse is given by the formula , where l is the length and w is the width, as shown in the diagram below. If the length is 4 feet and the width is 3 feet, what is the outside perimeter of the ellipse in feet?

（A）π （B） (4 + 3) （C） π （D） (4π + 3) （E） 5π

What is the volume, in cubic centimeters, of a cone with a height of 9 centimeters and a base with a radius of 4 centimeters? (The volume of a cone is , where R is the radius of the base of the cone and h is the height of the cone.)

（A）144π （B） 72π （C） 48π （D） 16π （E） 9π

The area of the square in the figure below is 324 square centimeters, and the two small isosceles right triangles are congruent. What is the combined area, in square centimeters, of the 2 small triangles?

(F) 108

(G) 162

(H) 216

(J) 324

(K) 648