Online Test — Areas Related to Circles
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
medium
If the perimeter and the area of a circle are numerically equal, then what is the radius of the circle?
1 unit
2 units
$\pi$ units
4 units
Explanation: $2\pi r = \pi r^2 \implies 2 = r$. Hence, radius must be 2 units.
Question 2 of 10
medium
What is the area of a circle whose total diameter is measured to be 14 cm?
44 sq. cm
154 sq. cm
616 sq. cm
77 sq. cm
Explanation: Radius is 7 cm. Area = $(22/7) \cdot 7 \cdot 7 = 154$ square cm.
Question 3 of 10
medium
Find the arc length of a sector of a circle with a radius of 21 cm and a central angle of 60 degrees.
11 cm
22 cm
44 cm
66 cm
Explanation: Arc length = $(60/360) \cdot 2 \cdot (22/7) \cdot 21 = (1/6) \cdot 132 = 22$ cm.
Question 4 of 10
medium
If the radius of a circle is doubled, what happens to its total interior area?
It doubles
It triples
It quadruples
It stays same
Explanation: Area depends on $r^2$, so doubling the radius scales area by $2^2 = 4$.
Question 5 of 10
medium
Find the area of a sector of a circle of radius 4 cm with a central angle of 90 degrees.
$2\pi$ sq. cm
$4\pi$ sq. cm
$\pi$ sq. cm
$8\pi$ sq. cm
Explanation: Area $= \frac{90}{360} \cdot \pi \cdot 4^{2} = \frac{1}{4} \cdot 16\pi = 4\pi$ sq. cm.
Question 6 of 10
medium
A region bounded by a straight chord line and its corresponding boundary arc is called a...
Sector
Segment
Quadrant
Tangent
Explanation: By structural definition, a chord and arc enclose a circle segment.
Question 7 of 10
medium
If a sector has a central angle of 180 degrees, it is geometrically known as a...
Quadrant
Segment
Semicircle
Chord
Explanation: An angle of 180 degrees cuts a circle exactly in half, forming a semicircle.
Question 8 of 10
medium
Find the perimeter of a semicircle protractor whose radius is 7 cm.
22 cm
36 cm
44 cm
29 cm
Explanation: Perimeter = Curved arc + straight diameter = $\pi r + 2r = 22 + 14 = 36$ cm.
Question 9 of 10
medium
The area of a sector with a central angle of $\theta$ degrees and radius $r$ is equal to...
$(\theta/180) \cdot \pi r^2$
$(\theta/360) \cdot 2\pi r$
$(\theta/360) \cdot \pi r^2$
$(\theta/720) \cdot \pi r^2$
Explanation: This matches the standard fractional area formula for a sector.
Question 10 of 10
medium
To find the area of a minor segment, what shape must you subtract from the sector area?
A rectangle
A triangle
A smaller circle
A square
Explanation: Subtracting the interior triangle leaves the curved outer segment area.