12 multiple-choice questions, progressively harder.
A circle of diameter 12.812.812.8 cm is dilated by 3/43/43/4. Which pair describes the image circle?
Solution
Correct answer: B
Dilation multiplies both lengths by the same positive factor.
That factor cancels in the ratio, which remains π\piπ.
A circle has radius 15/415/415/4 cm. What is its exact circumference?
Correct answer: D
Circumference is twice pi times the radius.
A circle has diameter 727\sqrt272 cm. What is its exact area?
Correct answer: A
Halve the diameter, then square the radius.
A circle has circumference 19π19\pi19π cm. What is its radius?
Correct answer: C
Divide by twice pi, not by pi alone.
One circle is the 4/34/34/3 dilation of another. Which pair gives the circumference factor and the area factor, respectively?
Circumference scales as a length. Area scales by the square of the length factor.
An inscribed polygon has perimeter 171717 cm and a circumscribed tangent polygon has perimeter 191919 cm. Which open interval must contain the circle's circumference?
The straight inner boundary is shorter than the circular boundary, while the tangent outer boundary is longer.
A regular hexagon is inscribed in a radius-2.52.52.5 cm circle. Its six sides equal the radius. What is the hexagon's perimeter?
Add the six equal straight sides.
This is the polygon perimeter, not the circumference.
A regular hexagon has perimeter 969696 cm and apothem 838\sqrt383 cm. What is its area?
Its center-triangles all have the apothem as height.
For a circle, C=75πC=75\piC=75π cm and d=75d=75d=75 cm. What units does the ratio C/dC/dC/d have?
Use the same length unit in numerator and denominator.
The length units cancel.
Certified bounds give 51.2001<C<51.200951.2001<C<51.200951.2001<C<51.2009, in centimeters. The midpoint estimate is 51.200551.200551.2005 cm. Which is the smallest guaranteed strict error bound among these choices?
The largest possible distance from the midpoint is half the interval width.
The endpoints are excluded, so the error is strictly smaller.
A disk has area 121π/9121\pi/9121π/9 square centimeters. What is its diameter?
Recover the positive radius before doubling it.
A disk is cut into 323232 equal curved wedges and the pieces are rearranged without gaps or overlaps between their interiors. Which statement is correct about that finite rearrangement?
Cutting and rigidly moving pieces preserves their total area. It does not straighten their circular arcs. A finite row is an approximation to a parallelogram, not an exact one.
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