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

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

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

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

None

If sin A = b, what is the value of the product sin A · cos A · tan A in terms of b?

b²

1/b

None

If 0<x, y<π/2 , and sin x = cos y, then which of the statements below must
be true?
I. x = y
II. 2(x + y) = π
III. cos x = sin y

II and III only

III only

II only

I and II only

None

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

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

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

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

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

None

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

4√2 +4

4√3

4√2

None

A wedge-shaped piece is cut from a circular pizza. The radius of the
pizza is 14 inches and the angle of the pointed end of the pizza
measures 0.35 radians. The number of inches in the length of the
rounded edge of the crust is closest to which value?

5.7

4.0

7.5

4.9

None

What is the radian measure of the smaller angle formed by the hands
of a clock at 7 o’clock? 2π/3

7π/6

π/2

5π/6

2π/3

None

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?

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

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

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

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

None

The height of sand in a cylinder-shaped can drops 3 inches when 1
cubic foot of sand is poured out. What is the diameter, in inches, of the
cylinder?
2/√π

48/√π

2/√π

4/√π

16/π

None

10.

If x is an acute angle, which expression is not equivalent to cos x ?

−cos(−x)

cos(x − 2π)

$$(\frac{\pi}{2}-x)$$

−cos(x + π)

None

11.

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

–0.2

0.6

0.75

–0.6

None

12.

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

13.

The amount of light produced by a cylindrical fluorescent light bulb
depends on its lateral area. A certain cylindrical fluorescent light bulb
is 36 inches long, has a 1 inch diameter, and is manufactured to
produce 0.283 watts of light per square inch. What is the best estimate
for the total amount of light that it is able to produce?

40 watts

48 watts

32 watts

34 watts

None

14.

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=√r/π

s=r√π

s=π√r

s=√πr

None

15.

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?

x/2√π

π/√2x

x²/2π

√2x/π

None

16.

A box is constructed by cutting 3-inch squares from the corners of a
square sheet of cardboard, as shown in the accompanying diagram, and
then folding the sides up. If the volume of the box is 75 cubic inches,
find the number of square inches in the area of the original sheet of
cardboard.

121

None

17.

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

18.

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

19.

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?

16.5π

29π

33π

14.5π

None

20.

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

21.

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

−cos 1.39

cos 4.89

−cos 0.18

cos 4.53

None

22.

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

105

306

210

None

23.

If θ is an angle in standard position and its terminal side passes through the point
$\left ( \frac{\sqrt{3}}{2},\frac{1}{2} \right )$on the unit circle, then a possible value of θ is

$$\frac{11\pi}{6}$$

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

$$\frac{5\pi}{3}$$

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

None

24.

The unit circle above has radius OC, angle AOB measures w radians,
BA is tangent to circle O at A, and CD is perpendicular to the x-axis.
The length of which line segment represents sin w?

$$\bar{OD}$$

$$\bar{AB}$$

$$\bar{CD}$$

$$\bar{OB}$$

None

25.

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

26.

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?

133

111

122

110

None

27.

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

1 − sin x

1 − cos x

sin x + cos x

sin x − cos x

None

28.

Sophie has a hard rubber ball whose circumference measures 13
inches. She wants to store it in a box. What is the number of cubic
inches in the volume of the smallest cube-shaped box with integer
dimensions that she can use?

216

125

None

29.

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

6/13

7/17

7/18

7/12

None

30.

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 value of cos x?

1.2

0.8

1.5

1.6

None

Time's up

Mastering Geometry: SAT Geometry Quiz - part 2

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