Question 1

A circle with a circumference of

20\pi

cm is inscribed perfectly inside a square such that the circle touches all four sides. What is the area of this square?

Accepted Answer

400 square cm

Answer

80 square cm

Answer

314 square cm

Answer

100 square cm

Question 2

The side of a square is equal to the radius of a circle. If the area of the square is

20\pi

square units, what is the circumference of the circle in terms of

\pi

?

Accepted Answer

<math>14\pi</math> units

Answer

<math>49\pi</math> units

Answer

<math>7\pi</math> units

Answer

<math>28\pi</math> units

Question 3

A rectangle has a length of

20\pi

cm and a width of

\pi

cm. If a circle is drawn such that its circumference is equal to the perimeter of this rectangle, what is the radius of the circle (rounded to two decimal places)? Use

\pi \approx 3.14

.

Accepted Answer

6.37 cm

Answer

12.74 cm

Answer

40.00 cm

Answer

3.18 cm

Question 4

The circumference of a circular pond is

20\pi

meters. A rectangular walkway is built around a nearby garden with a width equal to the radius of the pond and a length equal to the diameter of the pond. What is the area of this rectangular garden?

Accepted Answer

72 square meters

Answer

36 square meters

Answer

144 square meters

Answer

24 square meters

Question 5

A circle has a circumference of

20\pi

cm. A rhombus is drawn such that its side length is equal to the radius of this circle and its height is

\pi

cm. What is the area of the rhombus?

Accepted Answer

40 square cm

Answer

80 square cm

Answer

64 square cm

Answer

20 square cm

Question 6

The area of a trapezoid is

20\pi

square units, and its height is

\pi

units. If the sum of the lengths of its parallel bases is equal to the radius of a specific circle, what is the circumference of that circle in terms of

\pi \approx 3.14

?

Accepted Answer

<math>40\pi</math> units

Answer

<math>10\pi</math> units

Answer

<math>60\pi</math> units

Answer

<math>20\pi</math> units

Question 7

The diameter of a circular tire is

20\pi

inches. A square floor tile has a perimeter that is exactly equal to the circumference of this tire. What is the area of the square floor tile? (Use

\pi

)

Accepted Answer

121 square inches

Answer

44 square inches

Answer

196 square inches

Answer

484 square inches

Question 8

The area of a parallelogram is

20\pi

square units and its base is

\pi

units. If the height of this parallelogram is equal to the radius of a circle, what is the circumference of that circle in terms of

\pi \approx 3.14

?

Accepted Answer

<math>10\pi</math> units

Answer

<math>25\pi</math> units

Answer

<math>5\pi</math> units

Answer

<math>20\pi</math> units

Question 9

The area of a square is

20\pi

square units. If the perimeter of this square is equal to the circumference of a circle, what is the radius of the circle in terms of

\pi

?

Accepted Answer

<math>16/\pi</math> units

Answer

<math>32/\pi</math> units

Answer

<math>8/\pi</math> units

Answer

<math>4/\pi</math> units

Question 10

The area of a rhombus is

20\pi

square cm and one of its diagonals is

\pi

cm. If the length of the other diagonal is equal to the diameter of a circle, what is the circumference of that circle in terms of

\pi \approx 3.14

?

Accepted Answer

16\pi cm

Answer

32\pi cm

Answer

8\pi cm

Answer

12\pi cm

Question 11

A circle with a circumference of

20\pi

cm is perfectly inscribed inside a square so that it touches all four sides. What is the area of this square?

Accepted Answer

400 square cm

Answer

314 square cm

Answer

100 square cm

Answer

200 square cm

Question 12

The perimeter of a rectangular garden is

20\pi

meters and its length is

\pi

meters. A circular fountain is placed in the center with a radius of

\pi \approx 3.14

meters. What is the area of the garden remaining around the fountain? (Use

\pi \approx 3.14

)

Accepted Answer

111.74 square meters

Answer

111.42 square meters

Answer

140.00 square meters

Answer

128.26 square meters

Question 13

A rectangle has a length of

20\pi

cm and a width of

\pi

cm. If a circle is drawn such that its circumference is equal to the perimeter of this rectangle, what is the radius of the circle? (Use

\pi \approx 3.14

)

Accepted Answer

6.37 cm

Answer

5.09 cm

Answer

20.00 cm

Answer

12.74 cm

Question 14

An athlete runs around a circular track 5 times, covering a total distance of

20\pi

meters. A square practice field has the same side length as the diameter of this circular track. What is the area of the square practice field? (Use

\pi

)

Accepted Answer

784 square meters

Answer

1225 square meters

Answer

196 square meters

Answer

400 square meters

Question 15

A trapezoid has a height of

20\pi

cm and parallel bases of

\pi

cm and

\pi \approx 3.14

cm. If a circle is drawn with a diameter equal to the height of this trapezoid, how much larger is the area of the trapezoid than the area of the circle? (Use

\pi \approx 3.14

)

Accepted Answer

69.76 square cm

Answer

70.44 square cm

Answer

120.00 square cm

Answer

50.24 square cm

Question 16

A rectangle has a length of

20\pi

cm and a width of

\pi

cm. If the circumference of a circle is numerically equal to the area of this rectangle, what is the radius of the circle? (Use

\pi \approx 3.14

)

Accepted Answer

12.74 cm

Answer

25.48 cm

Answer

80.00 cm

Answer

15.92 cm

Question 17

A circle has a circumference of

20\pi

cm. A rhombus is constructed such that its side length is equal to the radius of this circle. If the height of the rhombus is

\pi

cm, what is the area of the rhombus? (Use

\pi \approx 3.14

)

Accepted Answer

20 square cm

Answer

25 square cm

Answer

40 square cm

Answer

10 square cm

Question 18

The diameter of a circular pond is

20\pi

meters. A square wooden deck is built such that its perimeter is equal to the circumference of the pond. What is the area of the wooden deck? (Use

\pi

)

Accepted Answer

121 square meters

Answer

196 square meters

Answer

44 square meters

Answer

154 square meters

Question 19

The area of a square is

20\pi

square cm. A circle is drawn such that its diameter is equal to the side length of the square. What is the circumference of this circle? (Use

\pi

)

Accepted Answer

44 cm

Answer

88 cm

Answer

22 cm

Answer

154 cm

Question 20

A parallelogram has a base of

20\pi

cm and a height of

\pi

cm. A circle is created such that its circumference is equal to the area of this parallelogram. What is the approximate radius of this circle? (Use

\pi \approx 3.14

)

Accepted Answer

17.20 cm

Answer

34.39 cm

Answer

108.00 cm

Answer

14.52 cm

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