Geometry Problems of the Day

The following problems were taken from the GEOMETRY (COMMON CORE) Regents Exam given on Thursday, January 26, 2017.
Previous problems can be found here.

Part 1

11. A solid metal prism has a rectangular base with sides of 4 inches and 6 inches, and a height of 4 inches. A hole in the shape of a cylinder, with a radius of 1 inch, is drilled through the entire length of the rectangular prism.

What is the approximate volume of the remaining solid, in cubic inches?

(2) 77.
The Volume of the prism is 4 x 4 x 6 or 96 cubic inches. The Volume lost by drilling the cylinder is (1)²(pi)(6), which is approximately 18.85. Subtract 96 - 19 = 77.

12. Given the right triangle in the diagram below, what is the value of x, to the nearest foot?

(3) 18
Cos (40) = 14 / x.
so x = 14 / cos (40) = 18.3
Make sure your calculator is in Degree mode.




Continue to the next problems.