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SAT Math : How to find the length of the diameter

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Example Questions

Example Question #43 : Circles

The area of a circle is $144\Pi$ $\displaystyle 144\Pi$ . Find the diameter.

Possible Answers:

$\displaystyle 24$

$\displaystyle 12$

$\displaystyle 20$

$\displaystyle 36$

$\displaystyle 6$

Correct answer:

$\displaystyle 24$

Explanation:

The formula for the area of a circle is

$A = \Pi r^2$ $\displaystyle A = \Pi r^2$

with r being the length of the radius.

Since we know that the area of the circle is

$144\Pi$ $\displaystyle 144\Pi$

we can solve for r and get 12. (Do so by canceling out the two pi's and taking the square root of 144). Once we know the radius, we can easily find the diameter, since the diameter is twice the length of the radius. Therefore, the diameter is 24, as

$12\cdot2 = 24$ $\displaystyle 12\cdot2 = 24$

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Example Question #51 : Circles

Give the diameter of a circle with radius forty-two inches.

Possible Answers:

$6\textrm{ ft}$ $\displaystyle 6\textrm{ ft}$

$8\textrm{ ft}$ $\displaystyle 8\textrm{ ft}$

$5\textrm{ ft}$ $\displaystyle 5\textrm{ ft}$

$7\textrm{ ft}$ $\displaystyle 7\textrm{ ft}$

None of these

Correct answer:

$7\textrm{ ft}$ $\displaystyle 7\textrm{ ft}$

Explanation:

The diameter of a circle is twice its radius, so if a circle has radius 42 inches, its diameter is

$42 \textrm{ in} \times 2 = 84 \textrm{ in}$ $\displaystyle 42 \textrm{ in} \times 2 = 84 \textrm{ in}$

Divide by 12 to convert to feet:

$84 \textrm{ in } \div 12 \textrm{ in/ft} = 7 \textrm{ ft}$ $\displaystyle 84 \textrm{ in } \div 12 \textrm{ in/ft} = 7 \textrm{ ft}$

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SAT Math : How to find the length of the diameter

Study concepts, example questions & explanations for SAT Math

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Example Question #43 : Circles

Example Question #51 : Circles

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