OAR Math Skills: Geometry Questions and Answers — Questions and Answers
Question 1: A rectangular garden is 20 feet long and 15 feet wide. A circular fountain with a diameter of 10 feet is placed in the exact center of the garden. Which of the following represents the area of the garden available for planting, in square feet? (Use π ≈ 3.14)
- 300 sq ft
- 221.5 sq ft (Correct answer)
- 78.5 sq ft
- 268.6 sq ft
Correct answer: 221.5 sq ft
First, calculate the total area of the rectangular garden: Area = length × width = 20 ft × 15 ft = 300 sq ft. Next, calculate the area of the circular fountain. The diameter is 10 feet, so the radius is half of that, which is 5 feet. The area of a circle is A = πr². So, the fountain's area is 3.14 × (5 ft)² = 3.14 × 25 sq ft = 78.5 sq ft. To find the planting area, subtract the fountain's area from the garden's total area: 300 sq ft - 78.5 sq ft = 221.5 sq ft.
Question 2: A painter leans a 13-foot ladder against a vertical wall. The base of the ladder is 5 feet away from the base of the wall. How high up the wall does the ladder reach?
- 10 feet
- 14 feet
- 12 feet (Correct answer)
- 18 feet
Correct answer: 12 feet
This scenario forms a right triangle, with the ladder as the hypotenuse (c), the distance from the wall as one leg (a), and the height up the wall as the other leg (b). Using the Pythagorean theorem (a² + b² = c²), we can solve for b. We have 5² + b² = 13². This simplifies to 25 + b² = 169. Subtract 25 from both sides: b² = 144. Taking the square root of both sides gives b = 12. The ladder reaches 12 feet up the wall.
Question 3: What is the volume of a cylindrical storage tank that has a radius of 3 meters and a height of 8 meters? (Use π ≈ 3.14)
- 75.36 m³
- 150.72 m³
- 226.08 m³ (Correct answer)
- 904.32 m³
Correct answer: 226.08 m³
The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Plugging in the given values: V = 3.14 × (3 m)² × 8 m. First, square the radius: 3² = 9 m². Then, multiply the values: V = 3.14 × 9 m² × 8 m = 226.08 m³.
Question 4: Two angles are supplementary. If one angle measures 65 degrees, what is the measure of the second angle?
- 25 degrees
- 115 degrees (Correct answer)
- 65 degrees
- 295 degrees
Correct answer: 115 degrees
Supplementary angles are two angles whose measures add up to 180 degrees. To find the measure of the second angle, subtract the measure of the known angle from 180: 180° - 65° = 115°. Therefore, the second angle measures 115 degrees.
Question 5: A rectangular field has a perimeter of 120 yards. If the width of the field is 25 yards, what is its area?
- 875 square yards (Correct answer)
- 950 square yards
- 1200 square yards
- 3000 square yards
Correct answer: 875 square yards
The formula for the perimeter of a rectangle is P = 2(l + w). We are given P = 120 and w = 25. So, 120 = 2(l + 25). Divide both sides by 2 to get 60 = l + 25. Subtract 25 from both sides to find the length: l = 35 yards. Now, calculate the area using A = l × w. A = 35 yards × 25 yards = 875 square yards.
Question 6: Which of the following is the correct formula for the sum of the interior angles of a polygon with 'n' sides?
- 360 / n
- 180 * n
- (n - 2) * 360
- (n - 2) * 180 (Correct answer)
Correct answer: (n - 2) * 180
The formula for calculating the sum of the interior angles of any convex polygon is (n - 2) × 180°, where 'n' is the number of sides. For example, a triangle (n=3) has (3-2) * 180 = 180 degrees. A quadrilateral (n=4) has (4-2) * 180 = 360 degrees.
OAR Math Skills: Geometry Questions and Answers
A rectangular garden is 20 feet long and 15 feet wide.
A circular fountain with a diameter of 10 feet is placed in the exact center of the garden.
Which of the following represents the area of the garden available for planting, in square feet? (Use π ≈ 3.14)