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Dig a hole shaped as a square with a length of 1 foot on the ceiling and cover it with a hemisphere. How many inches `should the diameter of the hemisphere be so that the hemisphere covers the hole completely? (1foot=12 inches)

Triangle RST is inscribed in the circle with circumference of 20π and ∠R>90°

Quantity A

ST

Quantity B

10




The radii of the above two circles are both 3. If these two circles intersect at point P and point Q and each circle pass through the center of the other circle, then what is the total perimeter of the region (not counting the arc inside)?
Give your answer to the nearest tenths.

The area of the square inscribed in the circle is 196, what is the area of the shaded region? (π≈3.14) Give your answer to the nearest tenths.

In the figure above, a square is inscribed in a circle, if the area of shaded region is 5π, what is the area of the square?
A stone was dropped into a still pond and produced concentric circular ripples on the surface of the water. The radius of the outermost ripple increased at a constant rate of x feet per second. If the area of the circular region enclosed by the outermost ripple was 400π square feet 10 seconds after the stone hit the water, what is the value of x?

If the length of the semi-circle fence is 20 feet, then what is the area of the fenced region in square feet?

An equilateral triangle PQR is inscribed in a circle. If the length of major arc PQR is 24 π, what is the radius of the circle?

In the sector OAC,∠O=90°, AC=8

Quantity A

The area of the sector OAC

Quantity B

4$$\sqrt{2}$$π



C is the center of the above circle. The length of DE equals to half of the radius of circle, and ∠ACD=90°.

Quantity A

The area of sector ABD with C at the center

Quantity B

The area of ACE



Q is the center of the circle.

QA=$$\frac{3}{2}$$QE
n=75, m=50

Quantity A

The length of arc ACB

Quantity B

The length of arc EDF



Arc AB is on the circle with center O, ∠AOB=90°

Quantity A

The area of the shaded region

Quantity B

The area of the semi-circle OCB with OB as its diameter



In the figure shown above, the area of the shadow is 12π, the small circle is inscribed in the big circle and pass the center of the big circle, what is the diameter of the small circle?
The length of a clock pendulum is 38, when the angle the pendulum goes is x degree, the length of arc it goes is 41, then what is the value of x?
Give your answer to the nearest tenths.

Four identical semi-circles overlap with a square on four sides, respectively. If the sides of the square is 4, and the entire figure is inscribed in a circle. What is the area of the shaded area?


Square ABCD is inscribed in the circle O and AB=2.

Quantity A

The area of ΔAOB

Quantity B

The area of shaded part



Quadrilateral ABCD is a parallelogram,r=2,and ∠DAB=45,what is the area of the shaded region?
In a xy-plane, the center of circle A is in circle B.
Quantity A: The number of intersects of circle A and B
Quantity B:1

As shown in the figure, there are 5 circles inscribed in a rectangle, each circle has a diameter of 4, and the circles are tangent to each other. What is the area of the rectangle?

Five identical small circles are inscribed in a larger circle, and the sum of the diameters of the 5 small circles equal the diameter of the larger circle.

Quantity A

The circumference of the large circle

Quantity B

The sum of the 5 circumferences of the smaller circle


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