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The garden is 10 meters long and 8 meters wide. A round pool with radi

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Joined: 02 Sep 2009
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The garden is 10 meters long and 8 meters wide. A round pool with radi  [#permalink]

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25 Sep 2019, 22:04
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Difficulty:

55% (hard)

Question Stats:

54% (01:41) correct 46% (02:05) wrong based on 24 sessions

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The garden is 10 meters long and 8 meters wide. A round pool with radius one meter has its center inside the garden. What is the probability that the whole pool is placed inside the garden (no part of the pool excesses the garden boundaries)?

A. 30%
B. 40%
C. 50%
D. 60%
E. 70%

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Joined: 18 Sep 2018
Posts: 64
Re: The garden is 10 meters long and 8 meters wide. A round pool with radi  [#permalink]

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25 Sep 2019, 23:29
IMO D

For the pool to be entirely inside,
the centre of the pool should be situated somewhere inside the area located with a length of (10-2) mts and a breadth of (8-2) mts..i.e. area = 48

Total area = 80

Probability = 48/80 = 60%

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Re: The garden is 10 meters long and 8 meters wide. A round pool with radi  [#permalink]

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29 Sep 2019, 19:07
Bunuel wrote:
The garden is 10 meters long and 8 meters wide. A round pool with radius one meter has its center inside the garden. What is the probability that the whole pool is placed inside the garden (no part of the pool excesses the garden boundaries)?

A. 30%
B. 40%
C. 50%
D. 60%
E. 70%

The area of the garden is 10 x 8 = 80.

The center of the pool has to be placed at least one meter inside each outer edge of the garden so that no part of the pool extends past the outer edge. Thus, we subtract 2 meters from the length of the garden and 2 meters from the width of the garden. This new restricting rectangle defines the allowable area in which the pool can be placed so that no part of it extends past the outer edge of the garden.

The area of this restricting rectangle 8 x 6 = 48

Thus the probability that the pool will not extend past the garden’s edge is 48/80 = 6/10 = 60%.

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Re: The garden is 10 meters long and 8 meters wide. A round pool with radi   [#permalink] 29 Sep 2019, 19:07
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