What is the total area that the tip of the boat can cover?

-

dock:

. . 6m
______
| . . . . |
| . . . . |
| . . . . | . 10m
| . . . . |
| . . . . |
|_____|

let boat tied top left corner rope 13 m long.

boat can form 3/4 circle of radius 13 13m below top left corner 13 m right of top left circle

once boat comes around bottom left corner, can form 1/4 circle of radius = 13-10 = 3
once boat comes around top right corner, can form 1/4 circle of radius = 13-6 = 7

total area = 3/4 (π*17²) + 1/4 (π * 3²) + 1/4 (π * 7²)
. . . . . . . .= 3/4 (289π) + 1/4 (9π) + 1/4 (49π)
. . . . . . . .= 925π / 4

total area = 726.49 m²

..

there stationary dock in center of lake, rectangular dimensions 10m 6m. boat tied corner of dock , rope dock end of boat 13m dock.


Science & Mathematics Mathematics Next



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