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Area and volume SAT question

Math · Geometry and Trigonometry · Hard · Answer it here, explanation included.

Circle  has a radius of and circle  has a radius of , where is a positive constant. The area of circle  is how many times the area of circle ?

ExplanationShow

Choice D is correct. The area of a circle can be found by using the formula , where is the area and is the radius of the circle. It’s given that the radius of circle A is . Substituting this value for into the formula  gives , or . It’s also given that the radius of circle B is . Substituting this value for into the formula gives , or . Dividing the area of circle B by the area of circle A gives , which simplifies to . Therefore, the area of circle B is times the area of circle A.

Choice A is incorrect. This is how many times greater the radius of circle B is than the radius of circle A.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is the coefficient on the term that describes the radius of circle B.

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