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555-605 (Medium)|   Geometry|      
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Shubhradeep
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The centre of a giant spherical meteoroid of radius 4 km fell inside 29 Feb 2024, 10:14
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45% (medium)

Question Stats:

38% (01:42) correct 63% (01:39) wrong based on 8 sessions

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­The centre of a giant spherical meteoroid of radius 4 km fell inside a biodiversity park and destroyed everything within its radius. What is probability that the meteoroid breaks the boundary of the park if the diameter of the park is 24 km.

A. \(\frac{5}{9}\)

B. \(\frac{4}{9}\)

C. \(\frac{1}{4}\)

D. \(\frac{5}{8}\)

E. \(\frac{1}{3}\)­
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stne
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The centre of a giant spherical meteoroid of radius 4 km fell inside 02 Mar 2024, 11:30
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Quote:
The centre of a giant spherical meteoroid of radius 4 km fell inside a biodiversity park and destroyed everything within its radius. What is probability that the meteoroid breaks the boundary of the park if the diameter of the park is 24 km.

A. \(\frac{5}{9}\)

B. \(\frac{4}{9}\)

C. \(\frac{1}{4}\)

D. \(\frac{5}{8}\)

E. \(\frac{1}{3}\)­
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­
Only if the meteroid falls in the red region will the boundry be broken. Please refer to the attached fig.

\(\pi (12)^2 -\pi (8)^2 = 144\pi - 64\pi = 80\pi\) = area of red region.

 Total area of park \(= \pi (12)^2 = 144\pi \)

Probability \(= \frac{80 \pi}{144 \pi} = \frac{5 }{9}\)

Ans A 

Hope it helped.­­­­­­­­­­­­­­­

*fig not to scale­­­­­­
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