The area of the largest circle that can be drawn inside a rectangle with sides 18cm by 14cm is

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RRB ASSISTANT LOCO PILOT (Allahabad) 2010 click here to view all questions

The area of the largest circle that can be drawn inside a rectangle with sides 18cm by 14cm is

A49 $cm^2$

B154 $cm^2$

C378 $cm^2$

D1078 $cm^2$

subash ? Dec 23 '2019 at 17:59

Correct answer is:  \(154 \text{ }cm^2\)

Explanation:

The diameter is equal to the shortest side of the rectangle.

 So radius= \(\frac{14}{2} = 7cm. \)

Therefore, \(area\;of\;circle\;=\mathrm{πr}^2=\frac{22}7\times49=154\mathrm{cm}^2\)

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If the length and breadth of a rectangle are in the ratio 3 : 2 and its perimeter is 20 cm, then the area of the rectangle (in cm^{2}) is

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RRB ASSISTANT LOCO PILOT (Allahabad) 2010 click here to view all questions

If the length and breadth of a rectangle are in the ratio 3 : 2 and its perimeter is 20 cm, then the area of the rectangle (in $cm^2$) is

A24 $cm^2$

B36 $cm^2$

C48 $cm^2$

D12 $cm^2$

suresh ? Dec 23 '2019 at 16:43

Correct answer is: \(24 \text{ } cm^2\)

Explanation:

\(\Large 2(l+b)=20cm\)

\(\Large 2(3x+2x)=20cm\)
\(\Large 2 \times 5x=20cm\)

\(\Large 10x=20\)

\(\Large x=2\)

\(\therefore length = 3 \times 2=6cm\)

\(breadth = 2 \times 2=4cm\)

\(area = length \times breadth\)

\(\Large =6 \times 4=24 \text{ } cm^{2}\)

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If the radius of a circle is increased by 50%, then the area of the circle is increased by

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RRB ASSISTANT LOCO PILOT (Allahabad) 2010 click here to view all questions

If the radius of a circle is increased by 50%, then the area of the circle is increased by

A1.25

B1

C0.75

D0.5

rajesh ? Dec 22 '2019 at 21:34

Correct answer is: 1.25

Explanation:

\(\Large \left[ \frac{ \pi r^{2} \left(2.25-1\right) }{ \pi r^{2}} \right] = 1.25\)

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If the volume of two cubes are in the ratio of 27 : 64, then the ratio of their total surface area is

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RRB GG Exam (Bhopal) 2009 click here to view all questions

If the volume of two cubes are in the ratio of 27 : 64, then the ratio of their total surface area is

A27 : 64

B3 : 4

C9 : 16

D3 : 8

prasad ? Dec 20 '2019 at 17:9

Correct answer is:  9 : 16

Explanation:

\(\Large \frac{(a_{1})^{3}}{(a_{2})^{3}}=\frac{27}{64}\)

\(\Large \frac{a_{1}}{a_{2}}=\frac{3}{4}\)

Ratio of their total surface area

\(\Large =\frac{6a_{1}^{2}}{6a_{2}^{2}}= \left(\frac{a_{1}}{a_{2}}\right)^{2}\)

\(\Large = \left(\frac{3}{4}\right)^{2}=\frac{9}{16}=9:16\)

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The area of a rhombus with diagonals 12cm and 20cm is — sq cm.

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RRB ASM Exam (Bhubaneshwar) 2009 click here to view all questions

The area of a rhombus with diagonals 12cm and 20cm is — sq cm.

A120

B12

C20

D240

task bot ? Jan 8 '2019 at 21:59

Answer is : A [120]

Explanation:

Let the one diagonal be x
area of rhombus = \(\frac{1}{2} \times d1 \times d2\)
area = \(\frac{1}{2} \times 20 \times 12\)
area = 120

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