A circular swimming pool has diameter 50 feet and is centered in a fenced-in square region measuring 90 feet by 90 feet. Aconcrete sidewalk 5 feet wide encircles the pool, and the rest of the region is grass, as shown in the figure below. (Roundyour answers to one decimal place.)poolsidewalkgrass(a) Find the surface area of the water.ft2(b) Find the area of the concrete sidewalk.ft2(c) Find the area of the grass.ft2

Given: A circular swimming pool has a diameter of 50 feet. Swimming pool is centered in a fenced…

Answered: A circular swimming pool has diameter…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

A circular swimming pool has diameter 50 feet and is centered in a fenced-in square region measuring 90 feet by 90 feet. A
concrete sidewalk 5 feet wide encircles the pool, and the rest of the region is grass, as shown in the figure below. (Round
your answers to one decimal place.)
pool
sidewalk
grass
(a) Find the surface area of the water.
ft2
(b) Find the area of the concrete sidewalk.
ft2
(c) Find the area of the grass.
ft2

Expert Solution

Step 1

Given:

A circular swimming pool has a diameter of 50 feet.
Swimming pool is centered in a fenced square region measuring 90 by 90 feet.
A concrete sidewalk of 5 feet wide encircles the pool.

The surface area of the water can be calculated as,

$S_{water} = \frac{π {d_{1}}^{2}}{4} Here, d_{1} is the diameter of the inner circle whose value is 50 feet. = \frac{π {(50 feet)}^{2}}{4} = 1962.5 {ft}^{2}$

Hence, the surface area of the water is $1962.5 {ft}^{2} .$

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