Circumference and Circle Area: Practice Level 3 | Geometry

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

For one circle, the circumference is $2\pi(x-2)$ cm and the area is $\pi(7x-20)$ square cm. Which real x-values can describe this circle?

Answer choices for question 1 A $-3$ and $-8$ B $2$ and $7$ C $8$ only D $3$ and $8$
2

For a circle measured in centimeters, the numerical area in square centimeters is thirteen times the numerical circumference in centimeters. What is its radius?

Answer choices for question 2 A $13$ cm B $26$ cm C $169$ cm D $52$ cm
3

AB is a diameter, C lies on the circle, AC is 9 cm, and BC is 12 cm. What is the disk's exact area?

Answer choices for question 3 A $225\pi$ square cm B $21\pi/2$ square cm C $225\pi/4$ square cm D $81\pi/4$ square cm
4

Disk A has $5/8$ of disk B's area. What is circle A's circumference divided by circle B's circumference?

Answer choices for question 4 A $\sqrt{10}/4$ B $5/8$ C $25/64$ D $8/5$
5

Two circles have positive radii. Their circumference ratio, larger to smaller, is 5:2, and the radii differ by 6 cm. What is the sum of the disk areas?

Answer choices for question 5 A $196\pi$ square cm B $56\pi$ square cm C $116\pi$ square cm D $84\pi$ square cm
6

A circle has exact circumference 24.3 cm, and $3.14<\pi<3.15$ . Which interval is guaranteed to contain its radius, measured in centimeters?

Answer choices for question 6 A $\frac{24.3}{6.30}<r<\frac{24.3}{6.28}$ B $\frac{24.3}{3.15}<r<\frac{24.3}{3.14}$ C $\frac{6.28}{24.3}<r<\frac{6.30}{24.3}$ D $\frac{24.3}{(6.30)^2}<r<\frac{24.3}{(6.28)^2}$
7

An inner regular polygon has perimeter $P$ and positive apothem $h$ inside a radius- $r$ circle. The parallel-sided tangent polygon has perimeter $Pr/h$ . Which expression is the outer polygon area minus the inner polygon area?

Answer choices for question 7 A $\frac{P(r-h)}2$ B $\frac{P(r^2+h^2)}{2h}$ C $\frac{P(r^2-h^2)}{2r}$ D $\frac{P(r^2-h^2)}{2h}$
8

Certified bounds give $3.14158<\pi<3.14160$ . How does 22/7 compare with pi?

Answer choices for question 8 A $22/7=\pi$ B $22/7>\pi$ C $22/7<\pi$ D The bounds do not decide.
9

Two disks have circumferences $8\pi$ cm and $15\pi$ cm. Their combined material is reshaped into one disk without any area loss. What is the new circumference?

Answer choices for question 9 A $17\pi$ cm B $23\pi$ cm C $11.5\pi$ cm D $\pi\sqrt{23}$ cm
10

An estimate has guaranteed error at most 0.2 cm. Each refinement halves that error bound. What is the fewest refinements that make the bound less than 0.0001 cm?

Answer choices for question 10 A $10$ B $12$ C $11$ D $13$
11

Two circles have total circumference $34\pi$ cm and total disk area $169\pi$ square cm. What is the larger radius?

Answer choices for question 11 A $5$ cm B $12$ cm C $13$ cm D $17$ cm
12

Let $A$ be a disk area and let $T=Cr/2$ . Which information certifies that the absolute difference between A and T is less than 0.01 square unit?

Answer choices for question 12 A A and T round to the same integer. B One polygon has more than 24 sides. C An inner polygon has area below A. D Both A and T lie in the same interval whose width is less than 0.01.