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A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?Select one:a. 1120 m2b. 1250 m2c. 1210 m2d. 1200 m2

Question

A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?Select one:a. 1120 m2b. 1250 m2c. 1210 m2d. 1200 m2

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Solution

The area of grassy ground a calf can graze is determined by the length of the rope, which forms the radius of a circle around the stake to which the calf is tied. The formula for the area of a circle is πr².

  1. First, calculate the initial area the calf could graze when the rope was 12 m long. Area = πr² = π(12)² = 144π m²

  2. Then, calculate the new area the calf can graze when the rope is increased to 23 m. Area = πr² = π(23)² = 529π m²

  3. To find out how much additional grassy ground the calf can graze, subtract the initial area from the new area. Additional area = 529π - 144π = 385π m²

  4. To get the answer in decimal form, multiply the result by the value of π (approximately 3.14). Additional area = 385 * 3.14 = 1209.14 m²

So, the calf can graze an additional area of approximately 1209.14 m². The closest answer to this is 1210 m² (option c).

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