If the length of the diagonal of a square is 20cm, | Area Questions & Answers

Q:

Find the ratio of the areas of the incircle and circumcircle of a square.

A) 1:1	B) 1:2
C) 1:3	D) 1:4

Answer & Explanation Answer: B) 1:2

Explanation:

Let the side of the square be x. Then, its diagonal = $\sqrt{2 x^{2}} = \sqrt{2 x}$

Radius of incircle = $\frac{x}{2}$

Radius of circum circle= $\sqrt{2} \times \frac{x}{2} = \frac{x}{\sqrt{2}}$

Required ratio = $\frac{{πx}^{2}}{4} : \frac{{πx}^{2}}{2} = \frac{1}{4} : \frac{1}{2} = 1 : 2$

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Q:

A sector of 120, cut out from a circle, has an area of $\frac{66}{7} c m^{2}$ . Find the radius of the circle ?

A) 1	B) 2
C) 3	D) 4

Answer & Explanation Answer: C) 3

Explanation:

Let the radius of the circle be r cm. Then,

$\frac{120}{360} {πr}^{2} = \frac{66}{7}$

$r^{2} = \frac{66}{7} * \frac{7}{22} * 3$

r=3.

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Q:

Two concentric circles form a ring. The inner and outer circumferences of ring are $\frac{518}{7}$ m and $\frac{352}{7}$ m respectively. Find the width of the ring.

A) 4	B) 5
C) 6	D) 7

Answer & Explanation Answer: A) 4

Explanation:

Let the inner and outer radii be r and R metres.

Then $2 πR = \frac{352}{7} = > R = \frac{352}{7} * \frac{7}{22} * \frac{1}{2} = 8 m$

$2 πR = \frac{528}{7} = > R = \frac{528}{7} * \frac{7}{22} * \frac{1}{2} = 12 m$

=> Width of the ring = (R - r) = (12 - 8) m = 4 m.

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Q:

The inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle

A) 44	B) 22
C) 33	D) 84

Answer & Explanation Answer: D) 84

Explanation:

Let inner radius be r metres. Then, 2 $π$ r = 440 ; r = $440 \times \frac{7}{44}$ = 70 m.

Radius of outer circle = (70 + 14) m = 84 m.

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Q:

A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel.

A) 14	B) 13
C) 12	D) 11

Answer & Explanation Answer: A) 14

Explanation:

Distance covered in one revolution = $\frac{88 \times 1000}{1000}$ = 88m.

$2 {πR}^{2} = 88 \Rightarrow 2 \times \frac{22}{7} \times R = 88 \Rightarrow R = 88 \times \frac{7}{44}$

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Q:

The diameter of the driving wheel of a bus is 140 cm. How many revolution, per minute must the wheel make in order to keep a speed of 66 kmph ?

A) 150	B) 250
C) 350	D) 550

Answer & Explanation Answer: B) 250

Explanation:

Circumference = No.of revolutions * Distance covered

Distance to be covered in 1 min. = (66 X1000)/60 m = 1100 m.
Circumference of the wheel = 2 x (22/7) x 0.70 m = 4.4 m.
Number of revolutions per min. =(1100/4.4) = 250.

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Q:

The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.40 per metre.

A) 2808	B) 3808
C) 4808	D) 5808

Answer & Explanation Answer: D) 5808

Explanation:

Area = (13.86 x 10000) sq.m = 138600 sq.m

${πR}^{2} = 138600 \Rightarrow R^{2} = 138600 \times \frac{7}{22} \Rightarrow R = 210 m$

Circumference = $2 {πR}^{2} = 2 \times \frac{22}{7} \times 210 = 1320 m$

Cost of fencing = Rs. (1320 x 4.40) = Rs. 5808.

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Q:

The difference between two parallel sides of a trapezium is 4 cm. perpendicular distance between them is 19 cm. If the area of the trapezium is 475 find the lengths of the parallel sides.

A) 27 and 23	B) 24 and 23
C) 25 and 23	D) 22 and 23

Answer & Explanation Answer: A) 27 and 23

Explanation:

Let the two parallel sides of the trapezium be a cm and b cm.

Then, a - b = 4

And, $\frac{1}{2} \times (a + b) \times 19 = 475 = > (a + b) = 50$

Solving (i) and (ii), we get: a = 27, b = 23.

So, the two parallel sides are 27 cm and 23 cm.

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A) a	B) b
C) c	D) d

If the length of the diagonal of a square is 20cm,then its perimeter must be

a. $40 \sqrt{2}$ cm b. $30 \sqrt{2}$ cm c. 10cm d. 15 $\sqrt{2}$ cm

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If the length of the diagonal of a square is 20cm,then its perimeter must be a. 402cm b. 302cm c. 10cm d. 152cm

Quick Links

If the length of the diagonal of a square is 20cm,then its perimeter must be

a. $40 \sqrt{2}$ cm b. $30 \sqrt{2}$ cm c. 10cm d. 15 $\sqrt{2}$ cm