#SAT geometry part 2 - Sriwiszy Education

Mastering Geometry: SAT Geometry Quiz - part 2

The quiz consists of 200 questions, and the user will be presented with a unique set of 10 questions in each session for a diverse experience
Please note that answers cannot be deselected once chosen in the quiz, so make your choices carefully for an optimal testing experience.
Each question is meticulously crafted to mirror the complexity and diversity of geometric problem-solving you'll encounter in the SAT.
Use it as a targeted practice tool to identify and address specific areas of improvement.
Track your progress and see your geometric proficiency grow.

In the figure above of a right circular cone, what is the approximate number of cubic centimeters in the volume of the cone?

105

210

306

None

A bookend that weights 0.24 pounds is shaped like a pyramid with a
square base. How many pounds does a larger, similar pyramid-shaped
bookend weigh if it is made of the same material and each
corresponding dimension is 2 times as large?

3.75

4.75

6.75

5.75

None

What are the coordinates of the image of the point (1, 0) on the
terminal side of an angle after a counterclockwise rotation of 3/4π
radians?

$$\left ( -\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2} \right )$$

$$(-\sqrt{2},1)$$

$$\left ( -\frac{1}{2},\frac{1}{2} \right )$$

$$\left ( \frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2} \right )$$

None

The cylindrical tank shown in the diagram above is to be painted. The
tank is open at the top, and the bottom does not need to be painted.
Only the outside needs to be painted. Each can of paint covers 500
square feet. What is the least number of cans of paint that must be
purchased to complete the job?

None

The volume of a cylinder of radius r is 1/4 of the volume of a
rectangular box with a square base of side length x. If the cylinder and
the box have equal heights, what is r in terms of x?

π/√2x

√2x/π

x²/2π

x/2√π

None

The path traveled by a roller coaster is modeled by the equation y = 27
sin 13x + 30 where y is measured in meters. What is the number of
meters in the maximum altitude of the roller coaster?

None

In the figure above, if the edge length of the cube is 4, what is the shortest distance from A to D?

4√3

4√2 +4

4√2

None

In the unit circle above, an angle that measures 4 radians intercepts arc AB. What is the length of major arc AB?

$$\frac{\pi+2}{4}$$

$$\frac{4}{\pi}$$

$$\frac{\pi}{2}$$

None

If x = 1.75 radians, then the value of cos x is closest in value to which
of the following?

cos 4.53

−cos 0.18

cos 4.89

−cos 1.39

None

10.

The height h of a cylinder equals the circumference of the cylinder. In
terms of h, what is the volume of the cylinder?

h³/2

h³/4π

h² +4

h²/2π

None

11.

The slant height of a pyramid is the perpendicular distance from the vertex of the pyramid to the base of a triangular side. In the pyramid shown in the figure above, the height is labeled h, the length of a side of the square base is 24 cm, and the slant height is 15 cm. What is the volume, in cubic centimeters, of the pyramid?

1728

1234

1675

1342

None

12.

Which of the following expressions is equivalent to $\frac{\sin ^{2}x}{1+\cos x}$

1 − cos x

1 − sin x

sin x − cos x

sin x + cos x

None

13.

If x is a positive acute angle and cos x = a, an expression for tan x in
terms of a is

$$\frac{1}{1-a}$$

$$\frac{1-a}{a}$$

$$\sqrt{1-a^{2}}$$

$$\frac{\sqrt{1-a^{2}}}{a}$$

None

14.

A cylindrical tube with negligible thickness is placed into a rectangular
box that is 3 inches by 4 inches by 8 inches, as shown in the
accompanying diagram. If the tube fits exactly into the box diagonally
from the bottom left corner to the top right back corner, what is the best
approximation of the number of inches in the length of the tube?

9.4

7.8

3.9

5.5

None

15.

Two spheres that are tangent to each other have volumes of 36π cubic
centimeters and 972π cubic centimeters. What is the greatest possible
distance, in centimeters, between a point on one sphere and a second
point on the other sphere?

None

16.

The Parkside Packing Company needs a rectangular shipping box. The
box must have a length of 1 foot, a width of 8 inches, and a volume of
at least 700 cubic inches. What is the least number of inches in height
of the box such that the height is a whole number?

None

17.

A lamp shade with a circular base is an example of a solid shape called a frustrum. In the figure above, the shaded region represents a frustrum of a right cone in which the portion of the original cone that lies 12 inches below its vertex has been cut off by a slicing plane (not shown)
parallel to the base.
If the height and slant height of the frustrum are 8 inches and 10 inches, respectively, what is the number of inches in the radius length, R, of the original cone?

None

18.

In the unit circle above, the ordered pair (x, y) represents a point P where the terminal side intersects the unit circle, as shown in the accompanying figure. If θ= -π/3 radians, what is the value of y?

$$-\frac{\sqrt{2}}{2}$$

$$-\frac{1}{2}$$

$$-\frac{\sqrt{3}}{2}$$

$$-\sqrt{3}$$

None

19.

The dimensions of a rectangular box are integers greater than 1. If the
area of one side of this box is 12 and the area of another side is 15,
what is the volume of the box?

None

20.

If cos A = 4/5 and ∠A is not in Quadrant I, what is the value of sin A?

0.75

–0.6

0.6

–0.2

None

21.

A rod 6 inches long is pivoted at one end. If the free end of the rod
rotates in a machine at the rate of 165 revolutions per minute, what is
the total distance, in inches, traveled by the end of the rod in one
second?

33π

29π

16.5π

14.5π

None

22.

If cos θ =–3/4 and tan θ is negative, the value of sin θ is

$$\frac{\sqrt{7}}{4}$$

$$-\frac{\sqrt{7}}{5}$$

$$\frac{4\sqrt{7}}{7}$$

$$-\frac{4}{5}$$

None

23.

A wheel has a radius of 18 inches. The distance, in inches, the wheel
travels when it rotates through an angle of 2/5 π radians is closest to
which value?

None

24.

By law, a wheelchair service ramp may be inclined no more than
4.76°. If the base of a ramp begins 15 feet from the base of a public
building, which equation could be used to determine the maximum
height, h, of the ramp where it reaches the building’s entrance?

h=15 tan 4.76°

h=15 sin 4.76°

$$h= \frac{\tan 4.76°}{15}$$

$$h= \frac{15}{\sin 4.76°}$$

None

25.

In the figure above, θ is an angle in standard position and its terminal side passes through the point $p\left (-\frac{1}{2},\frac{\sqrt{3}}{2} \right )$ on the unit circle. What is a possible value of θ?

$$\frac{7}{6}\pi $$

$$\frac{4}{3}\pi $$

$$\frac{5}{6}\pi $$

$$\frac{2}{3}\pi $$

None

26.

A flagpole that stands on level ground. Two cables, r and s, are attached to the pole at a point 12 feet above the ground and form a right angle with each other. Cable r is attached to the ground at a point that makes tan x = 0.75.
What is the sum of the lengths of cables r and s?

None

27.

In the figure above, what is the value of sin A − cos A?

7/12

7/17

7/18

6/13

None

28.

If a pyramid with a square base with side length s and a right cone with
radius r have equal heights and equal volumes, then which equation
must be true?

s=π√r

s=r√π

s=√r/π

s=√πr

None

29.

A planned building was going to be 100 feet long, 75 feet deep, and 30
feet high. The owner decides to increase the volume of the building by
10% without changing the dimensions of the depth and the height.
What will be the new length of this building in feet?

110

111

122

133

None

30.

In the figure above, angles ACB and DEB are right angles, AC = 15,
CE = 12, and DE = 10. What is the value of cos x?

0.122

0.923

0.233

0.411

None

Time's up

SAT geometry part 2

Mastering Geometry: SAT Geometry Quiz - part 2

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Mastering Geometry: SAT Geometry Quiz - part 2

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