Home->ACT Math

The volume, V, of the right circular cone with radius r and height h, shown below, can be found using the formula V =  r 2h. A cone-shaped paper cup has a volume of 142 cubic centimeters and a height of 8.5 centimeters. What is the radius, to the nearest centimeter, of the paper cup?

(A)2

(B)4

(C)8

(D)12

(E)16

In the (x,y) coordinate plane below, points P (6,2) and Q (1,4) are two vertices of ΔPQR. If PQR is a right angle, then which of the following could be the coordinates of R?

(A) (4,-3) (B) (3, 0) (C) (2, 1) (D) (2, 4) (E) (3, 9)

Correct Answer: E

When calculating a certain tax, Simone found that no tax is due for all income up to pdollars, with p > 0. Income greater than pdollars is taxed at a rate of 15%. Which of the following graphs accurately represents this tax?

(A) (B) (C) (D) (E)

Correct Answer: B

A surveyor took and recorded the measurements shown in the figure below. If the surveyor wants to use these 3 measurements to calculate the length of the pond, which of the following would he find to be the most useful?

（A）The Pythagorean Theorem （B） The ratios for the side lengths of 30°-60°-90° triangles （C） The ratios for the side lengths of 45°-45°-90° triangles （D） The law of cosines, which states that for any ΔABC, where a is the length of the side opposite a, b is the length of the side opposite b, and c is the length of the side opposite c, a² = b² + c² - 2BC[cos （E） The law of sines, which states that the ratio between the length of the side opposite an angle and the sine of that angle is the same for all of the interior angles in the same triangle.

Correct Answer: D