The diagram shows a circular pond, of radius r metres, surrounded by a circular path.The circular path has a constant width of 1

Question

2 years ago

11

.5 metres.The area of the path is the area of the pond.(a) Show that 2r2 − 60r − 45 = 0

1 answer:

Alenkasestr [34] · Answer 1 · 2022-09-12T05:52:34+03:00

The formula for calculating the area of a circle is expressed as;

A = πr²

Since the area of the path is equal to the area of the pond, hence;

π(r+1.5)² - πr² = πr²

Add πr² to both sides

π(r+1.5)² - πr² + πr² = πr² + πr²

π(r+1.5)² = 2πr²

(r+1.5)² = 2r²

Expand the parenthesis

r²+3r + 2.25 = 2r²

r²+3r + 2.25 - 2r² = 0

-r² + 3r + 2.25 = 0

r² - 3r - 2.25 = 0

Multiply through by 2

2r² - 6.0r - 4.5 = 0

<em>This proves the required equation</em>

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Learn more on area of composite figures here: brainly.com/question/15981553