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Want to review SAT Mathematics but don’t feel like sitting for a whole test at the moment? Varsity Tutors has you covered with thousands of different SAT Mathematics flashcards! Our SAT Mathematics flashcards allow you to practice with as few or as many questions as you like. Get some studying in now with our numerous SAT Mathematics flashcards.

Flashcards: Working with Inscribed Shapes

Square A is inscribed inside Circle B which is then inscribed inside Square C. If the radius of Circle B is , what is the ratio of the area of Square A to the area of Square C?

1:4

1:2

2:3

1:3

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Flashcards: Working with Inscribed Shapes

Square A is inscribed inside Circle B which is then inscribed inside Square C. If the radius of Circle B is , what is the ratio of the area of Square A to the area of Square C?

Your answer:

1:4

Your answer:

2:3

Your answer:

1:3

Correct answer:

1:2

Explanation:

The diameter of Circle B will be the diagonal of the small Square A, but will be the length of the large Square C. You will use the diagonal information to determine the side of the small Square A, then you can calculate the area of each.

First, let's find the side of small Square A. If the radius of Circle B is , then the diameter is . You can use the diagonal to view Square A as two right isosceles ( 45-45-90 ) triangles. Since the hypotenuse of the triangle is , then the side of the triangle, and thus the side of Square A, is $\frac{2}{\sqrt{2}}$ . The area of this Square A is $(\frac{2}{{\sqrt{2}}})^{2}$ , which simplifies to $\frac{4}{2}$ , which then equals .

The diameter of Circle B is the same as the side of large Square C is . The area is .

The ratio of their areas is then 2:4 , which reduces to 1:2 .

Flashcards: Working with Inscribed Shapes

Screen shot 2020 09 15 at 3.16.25 pm

Square ABCD is perfectly inscribed in the circle pictured above. If minor arc AD measures $2\pi$ , what is the approximate area of the shaded region?

110

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Flashcards: Working with Inscribed Shapes

Screen shot 2020 09 15 at 3.16.25 pm

Square ABCD is perfectly inscribed in the circle pictured above. If minor arc AD measures $2\pi$ , what is the approximate area of the shaded region?

Your answer:

110

Your answer:

Correct answer:

Explanation:

To answer this question, you need to find the area of the circle and then subtract out the area of the square. If minor arc AD measures $2\pi$ then the entire circumference is $8\pi$ . This is because the arcs formed by the vertices of the square are each exactly $\frac{1}{4}$ of the circumference. If the circumference is $8\pi$ , then the radius is $(2\pi(r))=8\pi$ is how you'd calculate that). This then means that the area of the circle, $\pi(r^{2})$ , is $16\pi$ .

So you know everything there is to know about the circle, and now you need to move on to the square. For the square, simply draw in the diameter of the circle and realize that this is also the diameter of the square. Since the diagonal of any square is equal to a side of the square times $\sqrt{2}$ , the inverse is also true: the side of the square can be calculated as the diagonal divided by $\sqrt{2}$ . This the side of this square is equal to $\frac{8}{\sqrt{2}}$ , which can be simplified to $4\sqrt{2}$ .

The area of the square is side-squared, so that's $(4\sqrt{2})^{2}=32$ . So your answer here will be the area of the circle, $16\pi$ , minus the area of the square, . $16\pi$ is approximately , so the answer is approximately .

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Flashcards: Working with Inscribed Shapes

Flashcards: Working with Inscribed Shapes

Flashcards: Working with Inscribed Shapes

Flashcards: Working with Inscribed Shapes

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All SAT Mathematics Resources

Flashcards: Working with Inscribed Shapes

Flashcards: Working with Inscribed Shapes

Flashcards: Working with Inscribed Shapes

Flashcards: Working with Inscribed Shapes

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DMCA Complaint

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