A semicircle has a perimeter of 144 cm. What is its radius_________?
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Answer: B. 28 cm
Explanation
The perimeter formula for a semicircle includes both the curved arc length and the straight diameter base. Factoring out the radius leaves the expression r multiplied by the sum of pi and two. Solving the equation for r using twenty two over seven for pi yields a radius of twenty eight centimeters. Semicircle perimeter equals pi times radius plus two times radius representing the flat bottom edge. The constant pi is commonly approximated as twenty two over seven in geometric calculations. Isolating the radius variable requires dividing the total perimeter by the constant sum expression.
Architects and engineers calculate semicircle boundaries when designing arched windows and bridges. Landscaping design often incorporates semicircular garden beds requiring perimeter fencing calculations. Understanding curved geometric shapes is essential for advanced drafting and spatial design. Option A suggests twenty five centimeters which fails to satisfy the semicircle perimeter equation. Option C suggests thirty centimeters which overstates the radius derived from the perimeter sum. Option D suggests thirty five centimeters which produces a perimeter larger than one hundred forty four.
- Subject
- Mathematics
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- Mathematics
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- Difficulty
- medium
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