Joni has a circular garden with a diameter of 14 feet. If she uses 2 teaspoons of fertilizer for every 25 square feet of garden, how much fertilizer will Joni need for her entir…

Question

asked Nov 7, 2024 146k views

1 Answer

Jahnette · Answer 1 · 2024-11-12T00:59:10+0000

Answer:

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Explanation:

First, we need to find the area of the circular garden.

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The formula for the area of a circle is:

$\sf\qquad\dashrightarrow\rm{Area_((Circle)) = \pi r^2}$

where:

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So, in this case, the radius is:

$\rm\implies{Radius = (Diameter)/(2) = (14)/(2) = 7\: ft}$

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Substitute the given values into the given formula:

$\rm\implies{Area_((Circle)) = 3.14 * 7^2}$

$\rm\implies{Area_((Circle)) = 3.14 * 49}$

$\rm\implies{Area_((Circle)) = 153.86\: ft^2}$

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Now we can use the given information to find out how much fertilizer Joni needs.

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We know that she needs 2 teaspoons of fertilizer for every 25 square feet of garden.

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So, we can set up a proportion:

$\rm\implies{(2\: teaspoons)/(25\: ft^2) = (x\: teaspoons)/(153.86\: ft^2)}$

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Cross-multiplying, we get:

$\rm\implies{25x = 2 * 153.86}$

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Simplifying, we get:

$\rm\implies{25x = 307.72}$

$\rm\implies{\boxed{\boxed{\sf{\:\:\:x = \green{12.31\: teaspoons}\:\:\:}}}}$

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$\therefore$ Joni will need approximately 12.3 teaspoons of fertilizer for her entire garden.