MCQ

MCQ 11 Mark

Area of a rectangle and the area of a circle are equal. If the dimensions of the rectangle are $14 \ cm \times 11 \ cm,$ then the radius of the circle is

A
$21 \ cm$
B
$14 \ cm$
C
$10.5 \ cm$
✓
$7 \ cm$

Answer

Correct option: D.

$7 \ cm$

Area of a rectangle $=$ Area of a circle
Dimensions of the rectangle are $14 \ cm \times 11 \ cm$
Area of circle $= 14 \times 11 = 154 \ cm^2$
Then radius $=\sqrt{\frac{Area}{\pi}}=\sqrt{\frac{154 \times 7}{22}} \ cm$
$=\sqrt{7 \times 7} =7 \ cm$

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MCQ 21 Mark

The perimeter of a semicircle $($including its diameter$)$ of radius $7 \ cm$ is

A
$22 \ cm$
B
$29 \ cm$
✓
$36 \ cm$
D
$44 \ cm$

Answer

Correct option: C.

$36 \ cm$

The perimeter of a semicircle
$($including diameter$)$ of radius $7 \ cm$
$=\frac{1}{2} \times 2 \pi r+2 r=\pi r+2 r$
$=r(\pi+2)=7\left(\frac{22}{7}+2\right)$
$=7 \times \frac{22+14}{7}$
$=36 \ cm$

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MCQ 31 Mark

If the ratio of the radii of two circles is $3: 5$, then the ratio of their areas is

A
$3: 5$
B
$5: 3$
C
$25: 9$
✓
$9: 25$

Answer

Correct option: D.

$9: 25$

The ratio of radii of two circles is $3: 5$
Let radii of two circles be $3 x$, and $5 x$
Then ratio between then areas be
$\pi(3 x)^2: \pi(5 x)^2=97 \pi x^2: 25 \pi x^2$
$=9: 25$

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MCQ 41 Mark

If the ratio of the radii of two circles is $2$ then the ratio of their circumferences is

✓
$2: 3$
B
$3: 2$
C
$4: 9$
D
$9: 4$

Answer

Correct option: A.

$2: 3$

Let radii be $2 x$ and $3 x$
Then ratio between their
Circumferences $=2 \pi r_1: 2 \pi r_2$
$=2 \pi(2 x): 2 \pi(3 x)$
$=2 x: 3 x$
$=2: 3$

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MCQ 51 Mark

The area of a circle of diameter $d$ is

A
$2 \pi d^2$
B
$\pi d^2$
C
$\frac{\pi d^2}{2}$
D
$\frac{\pi d^2}{4}$

Answer

The area of a circle of diameter $d$ is $\pi r ^2=\pi\left(\frac{d}{2}\right)^2=\frac{\pi d^2}{4}$ (d)

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MCQ 61 Mark

If the area of a circle is numerically equal to its circumference, then the radius of the circle is

A
$1$ unit
✓
$2$ unit
C
$3$ units
D
$4$ units

Answer

Correct option: B.

$2$ unit

Area of a circle is numerically equal to its circumference the radius of the circle
$\pi r^2 = 2\pi r \Rightarrow r = 2$ units

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MCQ 71 Mark

The ratio of circumference to the area of a circle of radius $r$ units is

A
$2: r$
B
$r: 2$
C
$1: r$
D
$\pi: r$

Answer

The ratio of circumference to the area of a circle of radius $r$ units is $2 \pi r: \pi r^2=2: r(a)$

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MCQ 81 Mark

The circumference of the circle with diameter 28 cm is

A
44 cm
B
88 cm
C
176 cm
D
616 cm

Answer

The circumference of a circle with diameter
$28 cm \text { is }=28 \times \pi=28 \times \frac{22}{7}=88 cm \text { (b) }$

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MCQ 91 Mark

If the height of a parallelogram is doubled and base tripled, then its area becomes

A
2 times
B
3 times
C
6 times
D
12 times

Answer

If the height of a ||gm is doubled and base tripled then the area becomes 2 × 3 = 6 times $\text{(c)}$

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MCQ 101 Mark

If the base of a triangle is doubled and its height is halved, then the area of the resulting triangle

A
decreases
B
increases
C
doubles
D
emains the same

Answer

If the base is doubled and height is halved, then the area of the resulting triangle remains the same. (d)

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MCQ 111 Mark

If the area of a parallelogram is $54 cm ^2$ and the length of one side is $7.5 cm$, then the corresponding height is

A
$7.2 cm$
B
$14.4 cm$
C
$3.6 cm$
D
$13.5 cm$

Answer

Area of a $\| gm =54 cm ^2$
Length of one side $=7.5 cm$
Corresponding height $=\frac{\text { Area }}{\text { Side }}=\frac{54}{7.5}$
$=\frac{54 \times 10}{75}=\frac{36}{5}=7.2 cm$ (a)

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MCQ 121 Mark

If the perimeter of a square is $24 cm$, then its area is

A
$16 cm ^2$
B
$24 cm ^2$
C
$36 cm ^2$
D
$36 m ^2$

Answer

Perimeter of a square $=24 cm$
Side $=\frac{24}{4}=6 cm$
Area $=(\text { Side })^2=6 \times 6=36 cm ^2$ $\text{(c)}$

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