Question

I have a circular garden that is 40 feet in diameter. I need 5000 seeds to plant the whole garden. How many seeds would I need if the diameter of the garden were tripled?

Answer 1

Given :

• Diameter of circular garden = 40ft
• Number of seed planted = 5000
• Diameter of circular garden is tripled

To find :

Number of seed to be planted

Formula used :

Area of circle = πr²

Solution :

Seeds are planted in garden , that means along area.

Diameter of original circular garden = 40ft

Radius of original circular garden = 40ft/2 = 20ft

Now area of original circular garden = π(20ft)²

➝ Area of original circular garden = 400π ft²

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Diameter of new circular garden = 3× Diameter of original circular garden

Diameter of new circular garden = 3×40ft = 120ft

Radius of new circular garden = 120ft/2 = 60ft

Area of new circular garden = π(60ft)²

➝ Area of new circular garden = 3600π ft²

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Now we are given that 5000 seeds were planted in original circular garden

This means, in

$\sf \: Number \: of \: seeds \: planted \: in \: 400\pi \: ft ^{2} = 5000 \\ \\ \sf Number \: of \: seeds \: planted \: in \: 1 \: {ft}^{2} \: = \: \dfrac{5000}{400\pi} \\ \\ \sf Number \: of \: seeds \: planted \: in \: 3600\pi\: {ft}^{2} \: = \: \dfrac{5000}{400\pi} \times 3600\pi\\ \\ \sf Number \: of \: seeds \: planted \: in \: 3600\pi\: {ft}^{2} \: = \:5000 \times 9 \\ \\ \sf Number \: of \: seeds \: planted \: in \: 3600\pi\: {ft}^{2} \: = \: \bold{45000}$

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ANSWER : 45000 seeds