What is the area of a circle sector with a 5 cm radius formed by a 3.5 cm arc__________?
Show answer Hide answer
Answer: C. 8.75 cm2
Explanation
The area of a circle sector can be calculated directly using one-half multiplied by the arc length and the radius. Substituting the given values into the formula gives one-half times three point five centimeters times five centimeters. Evaluating this multiplication expression yields an exact sector area of eight point seventy-five square centimeters. A sector of a circle is a pie-shaped portion bounded by two radii and an enclosing arc along the circumference. The arc length formula relates the central angle to the total circumference of the circular boundary. Area formulas for circle sectors provide a shortcut when the arc length is known instead of the central angle.
Option A drastically underestimates the sector area by misplacing the decimal point during multiplication. Option B represents the area of a much larger sector or miscalculates the formula by omitting the one-half factor. Option D overestimates the area by confusing the sector formula with the total area of the full circle.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. A square's area is 4096 sq cm. Find the breadth-to-length ratio of a rectangle whose length is twice the square's side and breadth is 24 cm less than the side.
Show answer Hide answer
Answer: D. None of these
The square area of forty-forty-six means its side length is sixty-four centimeters. The rectangle length is twice the square side, giving one hundred twenty-eight centimeters. The rectangle breadth is twenty-four less th...
Q2. The average age of a husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is___________?
Show answer Hide answer
Answer: C. 40 years
The present combined age of all three family members is calculated by adjusting past age sums. Subtracting the current combined age of the wife and child from the total family age gives the answer. The husband's current...
Q3. The mean of 18 recorded values was computed as 124, but it was later found that figures 46 and 82 were logged incorrectly instead of 64 and 28. What is the corrected mean for the 18 records___________?
Show answer Hide answer
Answer: D. 122
The correct sum is found by subtracting incorrect logged values and adding correct values. The revised total sum equals 2232 minus 128 plus 92 resulting in 2196. Dividing the corrected sum by the total count of 18 record...
Q4. What is the maximum possible area of a triangle inscribed in a semicircle of radius R cm__________?
Show answer Hide answer
Answer: B. R2 cm2
The maximum area triangle inside a semicircle uses the semicircle diameter as its base. The height of this inscribed triangle equals the radius of the supporting semicircle. Multiplying one half by the base length and th...
Q5. Two similar triangles have areas of 12 cm2 and 48 sq cm. If the smaller triangle's height is 2.1 cm, what is the larger triangle's corresponding height_________?
Show answer Hide answer
Answer: B. 4.2cm
The ratio of areas of two similar triangles equals the square of their height ratio. The area ratio of 12 to 48 simplifies to one-fourth, making the height ratio one-half. Multiplying the smaller triangle height of 2.1 c...
Q6. Five numbers have a mean of 27. Excluding one number changes the mean to 25. What was the excluded number__________?
Show answer Hide answer
Answer: D. 35
Multiplying five numbers by their average mean gives the total sum of one hundred thirty five. Multiplying the remaining four numbers by their new mean gives the sum of one hundred. Subtracting the four number sum from t...