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puteri [66]
3 years ago
8

Lin and Tyler are drawing circles. Tyler’s circle has twice the diameter of Lin’s circle. Tyler thinks that his circle will have

twice the area of Lin’s circle as well. Do you agree with Tyler?
Mathematics
2 answers:
earnstyle [38]3 years ago
6 0
The answer would be No

Please thank
tatuchka [14]3 years ago
5 0

Answer:

No, tyler is wrong, his circle´s area has  four times the Lin’s circle area.

Step-by-step explanation:

Hello

Let's remember this about a circle

the area is given by:

A=\pi r^{2}

where r is the radius

and the diameter

D=2r\\isolating \ x\\r=\frac{D}{2}\\

Step 1

according to the question Tyler’s circle has twice the diameter of Lin’s circle,in other terms

Let

Tylers \ diameter\ (D_{1})  =2\ times\ Lins\ circle(D_{2})\\\\

D_{1}=2D_{2}

Step 2

find the areas

Area of Tyler’s circle

A_{1}=\pi  *r_{1} ^{2}

replacing

let r_{1}= Tyler’s circle radius

r_{1}=\frac{D_{1} }{2}  \\A_{1}=\pi  *r_{1} ^{2}\\A_{1}=\pi  *(\frac{D_{1} }{2})^{2}\\A_{1}=\pi *\frac{D_{1}^{2} }{4}

let\ r_{2}= Lin\ circle\ radiusr_{2}=\frac{D_{2} }{2}  \\A_{2}=\pi  *r_{2} ^{2}\\A_{2}=\pi  *(\frac{D_{2} }{2} )^{2}\\A_{2}=\pi *\frac{D_{2}^{2} }{4}\\\\

Now, from

D_{1}=2D_{2}\\so\\\D_{2}=\frac{D_{1} }{2}  \\

replacing

A_{2}=\pi *\frac{D_{2}^{2} }{4}\\A_{2}=\pi *\frac{(\frac{D_{1} }{2}) ^{2} }{4}\\\\\\

step 3

compare the areas

A_{1}=\pi *\frac{D_{1}^{2} }{4}\  and\ A_{2}= \pi *\frac{D_{1}^{2}}{16}\\\frac{A_{1}}{A_{2}} =\frac{\pi *\frac{D_{1}^{2} }{4}}{ \pi *\frac{D_{1}^{2}}{16}}\\\frac{A_{1}}{A_{2}} =4\\hence\\A_{1}=4 A_{2}

this means that  tyler is wrong, his circle´s area has  four times the Lin’s circle area.

Have a great day

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