Capgemini Geometry & Trigonometry Questions and Answers Quiz-1

1dm=0.1m
Thus 19m2.5dm=19.25 & 12m5dm=12.5m
Area of path with overlapping = (19.25m X 2m) + (12.50m X 2m) = 63.5 m^{2}
Since area of path is overlapped which is shaded in below figure. So, subtract 2m x 2m =4 m^{2}
Hence, the actual area of path = (63.5 m^{2} – 4 m^{2}) = 59.5 m^{2}(Answer)

 



Video solution:

Given information: In triangle pqr, pq=6 cm,pr=8 cm and qr=12 cm.

If a,b and c are three sides of a triangle, then by heron's formula area of the triangle is

Area=\sqrt{s(s-a)(s-b)(s-c)}

where,

s=\frac{a+b+c}{2}

The sides of triangle are 6, 8 and 12.

s=\frac{6+8+12}{2}=13

Area of triangle is

Area=\sqrt{13(13-6)(13-8)(13-12)}

Area=\sqrt{13(7)(5)(1)}

Area=\sqrt{455}

Area\approx 21.33

Therefore, the area of the triangle pqr is 21.33 square units.
Video Explanation:

2(a+b) = 18
(a+b)=9
\sqrt{a^{2}+b^{2}} = √41
(a+b)^{2} = a^{2}+b^{2} + 2ab
ab=20

Video Explanation:

Formula for rombus area is (diagonal 1 x diagonal 2)/2 thus

(8*10)/2 = 40 cm²

Video Explanation:

B
When t = -90 then (sin t, cos t) = (-1,0)
When t=0 then (sin t, cos t) = (0,1)
Plot above two points in x-y plane.

Area of rectangular plot = 112*78
=8736 m²
it has gravel path so, length = 112-2.5-2.5
=107m
breath = 78-2.5-2.5=73m
l*b= 107*73
=7811m²
area of path = 8736-7811
=925
cost of constructing = 925*2
= 1850 Rs

Volume of a sphere = (4/3) * pi * r^3 --(1) ( here r =3cm)
Volume of circular plate of thickness 1 cm is = pi * r^{2} * h -- (2)
( here h=1cm that is thickness )
Equating (1) and (2)
r=6cm

Video Explanation:

2990.4 m
Solution: let a is side of square field then a^{2}=31684
a=178
perimeter= 4 * a = 712
5% more than perimeter = 712 + 5% of 712 = 712 + 35.6 = 747.6
Because we enclose four times so 4 * 747.6 = 2990.4

volume of a hollow cylinder=pi*h*(R^{2}-r^{2})
22/7*21m*(36-25)m^{2}
=66*11m^{3}
=726 m^{3}

Video Explanation: