Geometry Problems of the Day (Geometry Regents, January 2014)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

Geometry Regents, January 2014

Part II: Each correct answer will receive 2 credits. Partial credit is possible.


29. The diameter of a sphere is 5 inches. Determine and state the surface area of the sphere, to the nearest hundredth of a square inch.

Answer:

The formula for the Surface Area of a Sphere is in the back of the booklet: SA = 4πr². The radius is HALF the diameter. To the nearest hundredth of a square inch means TWO decimal places.

SA = 4πr² = 4 (3.141592...)(2.5)² = 78.539...

The Surface Area is 78.54 square inches.

Note that if you didn't use enough accuracy for pi, such as only using 3.14, you will make a mistake.

30. Using a compass and straightedge, construct the perpendicular bisector of AB.
[Leave all construction marks.]

Answer:

To construct a perpendicular bisector, start at point A. Open you compass more than halfway to B. Make an arc centered on A. Move the compass to B without changing the size. Make an arc that overlaps the first arc. Use the straightedge to draw the perpendicular bisector.

31. The endpoints of AB are A(3,-4) and B(7,2). Determine and state the length of AB in simplest radical form.

Answer:

Use the Distance Formula, or Pythagorean Theorem. (They're related.) You can even make a sketch to find the distances between the x-coordinates and the y-coordinates.

d = SQRT ( (7 - 3)² + (-4 - 2)² )
d = SQRT ( 4² + (-6)² )
d = SQRT ( 16 + 36 )
d = SQRT ( 52 )

You are asked for "Simplest Radical Form" so DO NOT give a decimal, not one rounded to two places, not one with 8 significant digits followed by three dots.

The prime factors of 52 = 2 * 2 * 13 = 2² * 13

SQRT (2² * 13) = 2 * SQRT (13)

More to come. Comments and questions welcome.

More Regents problems.