Act Geometry Questions

The diagram below shows a pasture which is fenced in. All but 1 section of fence run straight north-south or east-west. Consecutive fence posts are 10 feet apart except for the 1 diagonal section. Which of the following statements best describes P, the perimeter of the pasture, in feet?

• P > 210 
• P < 210 
• P > 230
• P = 240

 If a central angle of measure 30° is subtended by a circular arc of length 6 meters, as is illustrated below, how many meters in length is the radius of the circle?

• π/36
• 36
• 36π
• 36/π

A rectangular box with a base 2 inches by 6 inches is 10 inches tall and holds 12 ounces of breakfast cereal. The manufacturer wants to use a new box with a base 3 inches by 5 inches. How many inches tall should the new box be in order to hold exactly the same volume as the original box? (Note: The volume of a rectangular box may be calculated by multiplying the area of the base by the height of the box.)

• 8
• 9
• 10
• 11

In the figure below, the circle centered at B is internally tangent to the circle centered at A. The smaller circle passes through the center of the larger circle and the length of AB is 5 units. If the smaller circle is cut out of the larger circle, how much of the area, in square units, of the larger circle will remain?

• 5π
• 10π
• 25π
• 75π

What is the length of y in this picture?

• 45
• 5√2
• 90
• 5

I have been given a hypotenuse in this 45-45-90 triangle.  How do I find the length of a leg of the triangle?

• Multiply by √2
• Divide by √2
• It's the same length as the hypotenuse.
• Divide by 2

Which side is the long leg in this 30-60-90 triangle?

• 4
• u
• v

Which side is the short leg of this 30-60-90 triangle?

• 6
• m
• n

I have been given the long leg in this 30-60-90 triangle.  How do I find the hypotenuse?

• Divide 8 by √3
• Divide 8 by 2
• Divide 8 by 2, then multiply that answer by √2
• Divide 8 by √3, then multiply that answer by 2

What are u and v in this 30-60-90 triangle?

• v = 2√3 u = 6
• v = 4 u = 4√3
• v = 4 u = 4√2
• v = 4√3 u = 8√3