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Question

The radius of circle A is r, and the radius of circle B is 3/4r. What is the ratio of the area of circle A to the area of circle B?

16 to 9

9 to 16

1 to 4

4 to 3

ANSWER : 1

Descrption

area of circle A is =&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>πr</mi><mn>2</mn></msup></math>area of circle B is =&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi><msup><mrow><mo>(</mo><mfrac><mrow><mn>3</mn><mi mathvariant="normal">r</mi></mrow><mn>4</mn></mfrac><mo>)</mo></mrow><mn>2</mn></msup></math>&nbsp;=&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>9</mn><mn>16</mn></mfrac><msup><mi>πr</mi><mn>2</mn></msup></math>ratio of area of circle A to circle B =&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mi>πr</mi><mn>2</mn></msup><mrow><mstyle displaystyle="true"><mfrac><mn>9</mn><mn>16</mn></mfrac></mstyle><msup><mi>πr</mi><mn>2</mn></msup></mrow></mfrac></math>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; =&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>πr</mi><mn>2</mn></msup><mo>&nbsp;</mo><mo>×</mo><mfrac><mn>16</mn><mrow><mn>9</mn><msup><mi>πr</mi><mn>2</mn></msup></mrow></mfrac></math>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 16/9 or &nbsp;16 to 9 (Ans)

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