Perimeter and Area Test

Result

Perimeter and Area Test - 40

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Question 1
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The outer circle has center $$O$$ and circumference $$p$$. $$OT$$ is a diameter of the inner circle.
The circumference of the inner circle $$\dfrac {1}{2}p$$

A
If the quantity in Column A is greater

B
If the quantity in Column B is greater

C
If the two quantities are equal

D
If the relationship cannot be determined from the information given

Solution

Let the radius of outer circle be $$r$$.
Circumference $$p$$ of outer circle is $$2 \times \pi \times r $$
$$ i.e. p = 2 \pi r$$.
Now the radius of inner circle is $$\dfrac {r}{2}$$, so the circumference of innercircle is $$2 \times \pi \times \dfrac {r}{2} = \pi \times r = \dfrac {p}{2}$$.
Therefore, the quantities in two columns are equal.
So, the correct option is $$C$$.
Question 2
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If one leg of an isosceles right-angled triangle is increased by $$6$$ cm and that of the other leg decreased by $$4$$ cm, then the area of the triangle decreases by $$24$$ sq cm. Find the length of the leg of the original triangle

A
$$36$$ cm

B
$$30$$ cm

C
$$24$$ cm

D
none of these

Solution
Question 3
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Find the area of the shaded region in the following figure

A
28. 45 sq. cm

B
113.6 sq. cm

C
59.8 sq. cm

D
46.88 sq. cm
Question 4
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In the figure above, the four circles have the same center and their radii are $$1, 2, 3$$ and $$4$$, respectively. What is the ratio of the area of the small shaded ring to the area of the large shaded ring?

A
$$1 : 2$$

B
$$1 : 4$$

C
$$3 : 5$$

D
$$3 : 7$$

Solution

We know that area of circle is $$ \pi \times {r}^{2}$$, where $$r$$ is radius.
Area of small shaded ring is $$ \pi \times ({ 2 }^{ 2 }-{ 1 }^{ 2 }) = \pi \times 3$$.
Area of large shaded region is $$ \pi \times ({ 4 }^{ 2 }-{ 3 }^{ 2 }) = \pi \times 7$$.
The ratio of smaller to larger shaded regions is $$ \pi \times \dfrac {3}{\pi }\times 7 = \dfrac {3}{7}$$.
Question 5
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A tire on a car rotates at 500 RPM (revolutions per minute) when the car is traveling at 50 km/hr (kilometers per hour). What is the circumference of the tire, in meters?

A
$$10\pi/6$$

B
$$50,000/(60*2\pi)$$

C
$$50,000/(500*2\pi)$$

D
$$10/6$$

Solution

Speed $$=50km/hr=50,000m/hr$$
speed $$(in \, m/min)=50,000/60\,m/min$$
In any given minute the car travels $$50,000/60m/min$$ and tire volutes $$500$$ times around or $$500$$ time its circumference.
Let the circumference be C.
$$\Rightarrow 50,000/60=500C$$
$$C=\dfrac{50,000}{500\times 60}$$
$$C=\dfrac{10}{6}m$$
Question 6
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The area of the given figure ABCDEF is

A
$$22.82$$ $$\displaystyle cm^{2}$$

B
$$25.82$$ $$\displaystyle cm^{2}$$

C
$$26.82$$ $$\displaystyle cm^{2}$$

D
$$28.82$$ $$\displaystyle cm^{2}$$
Question 7
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In the given figure, what is the area of $$\triangle PQR$$?

A
$$15\sqrt{3}\: cm^2$$

B
$$27\sqrt{5}\: cm^2$$

C
$$3\sqrt{15}\: cm^2$$

D
$$45\sqrt{3}\: cm^2$$
Question 8
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ABCD is a parallelogram, E is the mid-point of AB and CE bisects $$\displaystyle \angle BCD$$, the $$\displaystyle \angle DEC$$ is:

A
$$\displaystyle { 60 }^{ \circ }$$

B
$$\displaystyle { 90 }^{ \circ }$$

C
$$\displaystyle { 100 }^{ \circ }$$

D
$$\displaystyle { 120 }^{ \circ }$$

Solution
Question 9
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Perimeter of circle is known as

A
Area

B
Volume

C
Diameter

D
Circumference
Question 10
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Circle $$C_1$$ passes through the centre of circle $$C_2$$ and is tangential to it. If the area of $$C_1$$ is $$4cm^2$$, then the area of $$C_2$$ is ________.

A
$$8cm^2$$

B
$$8\sqrt{\pi}cm^2$$

C
$$16cm^2$$

D
$$16\sqrt{\pi}cm^2$$