SAT Practice Questions  Geometry
Materials on this page relate to the SAT before March 2016.
For updated SAT materials, please see:
Try out the following Geometry Questions to help you prepare for the SAT, ACT or other similar examinations.
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Question 6
John has a square piece of paper with sides 4 inches each. He rolled up the paper to form a cylinder. What is the volume of the cylinder?
(A)


(B) 

(C) 
16 
(D) 
4π 
(E) 
16π 
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Question 7
The square ABCD touches the circle at 4 points. The length of the side of the square is 2 cm. Find the area of the shaded region.
(A)
(B)
(C)
(D)
(E) 
π – 4
2π – 4
3π – 4
4π – 4
5π – 4 
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Question 8
Note: Figures not drawn to scale
In the figure above, if x < 90° then which of the following must be true?
(A)


(B) 

(C) 
y < 90° 
(D) 
y = 90° 
(E) 
y > 90° 
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Solution:
Step 1: x and y are supplementary angles. So if x < 90° then y > 90°
Beware! Although the figure seems to show that l is parallel to m, it is not
stated in the question.
Answer: (E) y > 90°
Question 9
Note: Figures not drawn to scale
In the figure above, _{} and _{} and AE = EF . What is the value of x?
(A)
(B)
(C)
(D)
(E) 
40
45
50
55
60

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Solution:
Step 1: We can find the supplementary angle of 120°, which gives us 60°.
Step 2: is parallel to because they are both perpendicular to . This means that since they are corresponding angles.
Step 3: Triangle ABE and triangle ACF are similar triangles , since and (AA rule). Given that AE = EF, we can conclude that AB = BC
Step 4: Triangle ABE and triangle CBE are congruent triangles (SAS rule). So, x = angle AEB = 60°
So, x = 60
Answer: (E) 60
Question 10
In the figure above, if ∠AOB = 40° and the length of arc AB is 4π, what is the area of the sector AOB?
(A)
(B)
(C)
(D)
(E) 
4π
16π
36π
128π
324π

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Which segment is congruent to BE?
Which line has a slope of 3?
AD is parallel to BC. AC = 13, BC = 5, BD = 15. What is the length of AD?
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