Mensuration

A. 12 π cm
B. 16 π cm
C. 24 π cm
D. 32 π cm
Radius of larger circle
= 2×196−−−√=28cm
Circumference of smaller circle
= (37×28)cm=12cm
Circumference of smaller circle
= 2πr=2π×12= 24πcm

A. 23.57 cm
B. 47.14 cm
C. 84.92 cm
D. 94.94 cm
Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places

A. 3.34
B. 2
C. 4.5
D. 5.5
Area of the path = Area of the outer circle – Area of the inner circle = ∏{4/2 + 25/100}2 – ∏[4/2]2
= ∏[2.252 – 22] = ∏(0.25)(4.25) { (a2 – b2 = (a – b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m

A. 4192 sq m
B. 4304 sq m
C. 4312 sq m
D. 4360 sq m
Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 – ∏s2
= ∏{1762/∏2 – 1322/∏2}
= 1762/∏ – 1322/∏
= (176 – 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m

A. 200 sq cm
B. 72 sq cm
C. 162 sq cm
D. Cannot be determined
Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.

A. 18 : 5
B. 7 : 16
C. 5 : 14
D. None of these
Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4096 = 212
a = (212)1/2 = 26 = 64
L = 2a and b = a – 24
b : l = a – 24 : 2a = 40 : 128 = 5 : 16

A. 60 cm2
B. 30 cm2
C. 45 cm2
D. 15 cm2
The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2

A. 600 cm
B. 800 cm
C. 400 cm
D. 1000 cm
Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200 = 800 cm.

A. Rs. 3944
B. Rs. 3828
C. Rs. 4176
D. None of these
Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.

A. Rs. 3642.40
B. Rs. 3868.80
C. Rs. 4216.20
D. Rs. 4082.40
Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 – 0.04) = 4095 – 12.6 = Rs. 4082.40