The cross sectional area of a hemisphere is 2772 cm and its volume is 19404 cm . What is its radius?
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A.
21 cm
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B.
22.5 cm
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C.
42 cm
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D.
13 cm
Correct Answer:
A. 21 cm
Explanation:
To find the radius of the hemisphere, we can use the given cross-sectional area. In a hemisphere, the cross-section at its base is a circle. The formula for the area of this circle is A = πr². Given: - Cross-sectional area (A) = 2772 cm² - Using π ≈ 22/7Calculation:1. Set up the equation: 2772 = (22/7) \* r² 2. Isolate r²: r² = (2772 \* 7) / 22 3. Simplify: r² = 126 \* 7 4. r² = 882However, the question also provides the volume (19404 cm³). Let's use the volume formula for a hemisphere, V = (2/3)πr³, to verify or solve.1. 19404 = (2/3) \* (22/7) \* r³ 2. 19404 = (44/21) \* r³ 3. r³ = (19404 \* 21) / 44 4. r³ = 441 \* 21 5. r³ = 9261 6. r = ∛9261 7. r = 21 cmChecking the cross-sectional area again with r = 21: A = (22/7) \* 21 \* 21 = 22 \* 3 \* 21 = 1386 cm². Note: There is a discrepancy in the prompt's provided area (2772 is exactly double 1386, which would be the curved surface area, not the base cross-section). Based on the volume of 19404 cm³, the radius is consistently 21 cm. Correct Option: 21 cm (Option A)
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