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Area Problems

Area Problems
What is the diameter of the circle having 3 cm radius?

8 cm
6 cm
12 cm
1.5 cm

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Radius = Diameter/2 ? Diameter = 2 x Radius = 2 x 3 = 6 cm

Area Problems
The diagonal of a rectangle is √41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:

20 cm
41 cm
9 cm
18 cm

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

√l2 + b2 = √41. Also, lb = 20. (l + b)2 = (l2 + b2) + 2lb = 41 + 40 = 81 ⟹ (l + b) = 9. ∴ Perimeter = 2(l + b) = 18 cm

Area Problems
If the ratio of the area of two square is 9 : 1 the ratio of their perimeters is?

3:4
3:1
1:3
9:1

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Let the area of square be (9x)2 m2 and (x2) m2Then, their sides are (3x) m and x metres respectively? Ratio of their perimeters = 12x / 4x=3:1

Area Problems
The radius of a circle has been reduced from 9 cm to 7 cm . the appropriate percentage decrease in area is?

31.5 %
39.5 %
34.5 %
65.5 %

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Original area = (22/7) x 9 x 9 cm2New area = (22/7) x 7 x 7 cm2? Decrease = 22/7 x [(9)2 -(7)2] cm2=(22/7) x 16 x 2 cm2Decrease percent = [(22/7 x 16 x 2) /( 7/22 x 9 x 9)] x 100 %= 39.5 %

Area Problems
A rectangle has 30 cm as its length and 720 sq cm as its area. Its area is increased to 1 1/ 4 times its original area by increasing only its length. Its new perimeter is

119 cm
125 cm
123 cm
121 cm

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Original breadth of rectangle = 720/30 = 24 cmNow , area of rectangle = (5/4) x 720 = 900 cm2? New length of rectangle = 900/24 = 37.5 cm? New perimeter of rectangle = 2(l+ b)= 2(37.5 + 24 ) = 2 x 61.5 = 123 cm

Area Problems
If the radius of a circle be reduced by 50%. Its area is reduced by?

34.5%
65.5%
31.5%
39.5%

ANSWER EXPLANATION DOWNLOAD EXAMIANS APP

Original area = ? x (r/2)2 = ?r2/4Reduction in area = ? r2 - 3? r2/4? Reduction per cent = [ 3?r2/4 x 4/(?r2) x 100 ] %= 75%

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