Chief Editor
Chief Editor
 Mar 27, 2024
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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

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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:

$\sqrt{15}$

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The side length of a square is 55 centimeters (cm). What is the area, in cm${}^{2}$, of the square?
Difficulty: Easy
A:

110

B:

220

C:

3,025

D:

12,100

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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:

$2\pi$

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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

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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:

$128$

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A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?
Difficulty: Hard
A:

149,796

B:

164,500

C:

190,955

D:

310,800

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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:

$\frac{38}{15}$

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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:

$212^{\circ}$

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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

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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:

No additional information is necessary.

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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.

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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

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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:

$768\pi$

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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 $\pi$

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