##### A right circular cylinder has a volume of $45\,\pi$. If the height of the cylinder is 5, what is the radius of the cylinder?
Difficulty: Medium
A:

3

B:

4.5

C:

9

D:

40

##### In right triangle RST, the sum of the measures of angle $R$ and angle $S$ is 90 degrees. The value of $\sin(R)$ is $\frac{\sqrt{15}}{4}$. What is the value of $\cos(S)$?
Difficulty: Medium
A:

$\frac{\sqrt{15}}{15}$

B:

$\frac{\sqrt{15}}{4}$

C:

$$\frac{4\sqrt{15}}{15}$$

D:

$\sqrt{15}$

Difficulty: Easy
A:

110

B:

220

C:

3,025

D:

12,100

##### What is the length of one side of a square that has the same area as a circle with radius 2 ?
Difficulty: Medium
A:

2

B:

$\sqrt{2\pi}$

C:

$2\sqrt{\pi}$

D:

$2\pi$

##### Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X. What is the length, in centimeters, of one side of square Y?
Difficulty: Medium
A:

6

B:

10

C:

14

D:

24

##### The area of a square is $64$ square inches. What is the side length, in inches, of this square?
Difficulty: Easy
A:

$8$

B:

$16$

C:

$64$

D:

$128$

Difficulty: Hard
A:

149,796

B:

164,500

C:

190,955

D:

310,800

##### In triangle $ABC$, the measure of angle $B$ is $90^{\circ}$ and $\overline{BD}$ is an altitude of the triangle. The length of $\overline{AB}$ is $15$ and the length of $\overline{AC}$ is $23$ greater than the length of $\overline{AB}$. What is the value of $\frac{BC}{BD}$?
Difficulty: Hard
A:

$\frac{15}{38}$

B:

$\frac{15}{23}$

C:

$$\frac{23}{15}$$

D:

$\frac{38}{15}$

##### In $\bigtriangleup{XYZ}$, the measure of $\angle {X}$ is $24^{\circ}$ and the measure of $\angle{Y}$ is $98^{\circ}$. What is the measure of $\angle{Z}$?
Difficulty: Easy
A:

$58^{\circ}$

B:

$74^{\circ}$

C:

$122^{\circ}$

D:

$212^{\circ}$

##### Two nearby trees are perpendicular to the ground, which is flat. One of these trees is 10 feet tall and has a shadow that is 5 feet long. At the same time, the shadow of the other tree is 2 feet long. How tall, in feet, is the other tree?
Difficulty: Medium
A:

3

B:

4

C:

8

D:

27

##### In triangles $ABC$ and $DEF$, angles $B$ and $E$ each have measure $27^{\circ}$ and angles $C$ and $F$ each have measure $41^{\circ}$. Which additional piece of information is sufficient to determine whether triangle $ABC$ is congruent to triangle $DEF$?
Difficulty: Hard
A:

The measure of angle $A$

B:

The length of side $AB$

C:

The lengths of sides $BC$ and $EF$

D:

##### In triangles $LMN$ and $RST$, angles $L$ and $R$ each have measure $60^{\circ}$, $LN=10$, and $RT=30$. Which additional piece of information is sufficient to prove that triangle $LMN$ is similar to triangle $RST$?
Difficulty: Hard
A:

$MN=7$ and $ST=7$

B:

$MN=7$ and $ST=21$

C:

The measures of angles $M$ and $S$ are $70^{\circ}$ and $60^{\circ}$, respectively.

D:

The measures of angles $M$ and $T$ are $70^{\circ}$ and $50^{\circ}$, respectively.

##### A cube has an edge length of 41 inches. What is the volume, in cubic inches, of the cube?
Difficulty: Medium
A:

164

B:

1,681

C:

10,086

D:

68,921

##### A cylinder has a diameter of 8 inches and a height of 12 inches. What is the volume, in cubic inches, of the cylinder?
Difficulty: Medium
A:

$16\pi$

B:

$96\pi$

C:

$192\pi$

D:

$768\pi$

##### A manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of container A is 16 centimeters, and the radius of container B is 25% longer than the radius of container
Difficulty: Medium
A:

16,000 $\pi$

B:

20,000 $\pi$

C:

25,000 $\pi$

D:

31,250 $\pi$