# Regents Prep Geometry Polygons

Regents Prep Geometry Polygons: This examination has four parts, with a total of 38 questions. Students must answer all questions in this examination. Record your answers to the Part I multiple-choice questions on the separate answer sheet. Write your answers to the questions in Parts II, III, and IV directly in the booklet. All work should be written in pen, except for graphs and drawings, which should be done in pencil. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, e.t.c.

## Regents Prep Geometry Polygons

1.) What is the volume, in cubic centimeters, of a cylinder that has a height of 15 cm and a diameter of 12 cm?

• (A)130 Π
• (B) 540 Π
• (C) 750 Π
• (D) 997 Π

2.) In which polygon does that sum of the measures of the interior angles equal the sum of the measures of the exterior angles?

• (A) Triangle
• (B) Hexagon
• (C) Octagon

3.) If the surface area of a sphere is represented by 144 Π,  what is the volume in terms of Π?

• (A) 288 Π
• (B) 398 Π
• (C) 699 Π
• (D) 1250 Π
Answer:  (A) (Tips: Formula: 288 Π (Tips V=4/3Πr3 )

4.)The volume, in cubic centimeters, of a sphere whose diameter is 6 centimeters is

• (A) 12 Π
• (B) 24 Π
• (C) 36 Π
• (D) 48 Π
Answer:  (C) (Tips: Formula: V=4/3Πr3 )

5.) A right circular cylinder has an altitude of 11 feet and a radius of 5 feet. What is the lateral area, in square feet, of the cylinder to the nearest tenth?

• (A) 316.2
• (B) 348.8
• (C) 365.4
• (D) 345.6
Answer:  (D) (Tips: Formula: L=2Πrh )

6.) Which expression represents the volume, in cubic centimeters, of the cylinder represented in  the diagram below?

• (A) 582 Π
• (B) 972 Π
• (C) 1825 Π
• (D) 3259 Π
Answer:  (B) (Tips: Formula: V=Bh )

7.) A  right circular cylinder has a volume of 1,000 cubic inches and a height of 8 inches. What is the radius of the cylinder to the nearest tenth of an inch?

• (A) 6.3
• (B) 11.2
• (C) 19.8
• (D) 19.8
Answer:  (A) (Tips: Formula: V=Bh )

8.) In an equilateral triangle, what is the difference between the sum of the exterior anglesand the sum of the interior angles?

• (A) 1800
• (B) 1200
• (C) 900
• (D) 600
Answer:  (A) (Tips: Formula: sum ext= 3600)

9.) In the diagram below, a right circular cone has a diameter of 8 inches and a height of 12 inches. What is the volume of the cone to the nearest cubic inch?

• (A) 101
• (B) 201
• (C) 221
• (D)301
Answer:  (B) (Tips: Formula: V= 1/3 Bh)

10. A packing carton in the shape of a triangular prism is shown in the diagram below. What is the volume, in cubic, of this carton?

• (A) 20
• (B)120
• (C) 220
• (D) 320
Answer:  (B) (Tips: Formula: V= Bh)

11.) What is the measure of each interior angle of a regular hexagon?

• (A) 600
• (B) 1200
• (C) 1800
• (D) 3600
Answer:  (B) (Tips: Formula: 180 (n-2)/n)

Part II: Free-Response Questions

12.) Find, in degrees, the measures of both an interior angle an exterior angle of a regular pentagon.

13.) A right circular cone has a base with a radius of 15cm, a vertical height of 20 cm, and a slant height of 25cm. find, in terms of, the number of square centimeters in the lateral area of the cone.

14.)Tim is going to paint a wooden sphere that has a diameter of 12 inches. Find the surface area of the sphere, to the nearest square inch.

15.) The base of a pyramid is a rectangle with a width of 6 cm and a length of 8 cm. find, in centimeters, the height of the pyramid if the volume is 288 cm3.

16.) A regular pyramid with a square base is shown in the diagram below. A side, s, of the base of the pyramid is 12 meters, and the height, h, is 42 meters. What is the volume of the pyramid in cubic meters?

17.) The Parkside Packing Company needs a rectangular shipping box. The box must have a length of 11 inches and a width of 8 inches. Find to the nearest tenth of an inch, the minimum height of the box such that the volume is at least 800 cubic inches.

18.) A sphere has a diameter of 18 meters. Find the volume of the sphere, in cubic meters, in terms of Π.

19.) If the radius of the circular base of a right cylinder is 8 inches and height of the cylinder is 20
inches, answer each of the following questions. Show all formulas and all work. Leaver any answer that involves Π, in terms of Π.

a) Find the area of the circular base of the cylinder.
b) Find the lateral area of the cylinder.
c) Find the surface area of the cylinder.
d) Find the volume of the cylinder.