*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.

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