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# The area of a circle with radius a is less than the area of

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The area of a circle with radius a is less than the area of [#permalink]  07 Nov 2019, 10:50
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52% (00:47) correct 47% (01:13) wrong based on 34 sessions
The area of a circle with radius $$a$$ is less than the area of a square with sides of length $$ka$$. Which of the following could be the value of k?

Indicate all such values.

A. $$\frac{4}{3}$$

B. $$\frac{5}{3}$$

C. $$\frac{6}{3}$$

D. $$\frac{7}{3}$$
[Reveal] Spoiler: OA

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Re: The area of a circle with radius a is less than the area of [#permalink]  23 Nov 2019, 16:58
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Area of the circle a²*pi
area of the square a²k²
k² is greater than pi
k is greater than the square root of pi

Answer is C and D (both greater than or equal to the square root of pi)
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Re: The area of a circle with radius a is less than the area of [#permalink]  14 Jun 2020, 06:20
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The area of a circle with radius a is less than the area of a square with sides of length ka. Which of the following could be the value of k?

Area of circle = pi * r^2
where r = a
so Area = pi*a^2

Area of square = Side^2
so Area of square = k^2 * a^2

equate together,
pi*a^2 = k^2 * a^2
simplify
pi=k^2
we know that, pi = 3.142
so search for those given values of k that prove pi<k^2
only 6/3 and 7/3 are those values
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Re: The area of a circle with radius a is less than the area of   [#permalink] 14 Jun 2020, 06:20
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