TCS Geometry Questions 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:

we know s=\frac{(a+b+c)}{2}
here a=6cm, b=8cm , c=12cm
therefore s=\frac{(6+8+12)}{2}
=13
area of tringle=sqrt {[ s (s-a) (s-b) (s-c)]}
=\sqrt {[ 13\times (13-6) \times (13-8)\times (13-12)]}
=\sqrt{[ 13\times 7\times 5\times 1]}
=\sqrt {[455]}
=21.33 cm^{2}

Video Explanation:

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

(a +b)^{2} = a^{2} +b^{2} +2ab
81 = 41 + 2ab

ab=20cm^{2}

Video Explanation:

Formula for rombus area = \frac{1}{2}\times 8\times 10

= 40 cm^{2}

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.
Answer: Option 4

Area of the path = (112 x 78) – (73  x 107) = 925 m^{2}

Video Explanation:

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

The formula for finding the number of sides in a polygon is d = \frac{n(n-3)}{2}

Where n is the number of sides.

77 = \frac{n(n-3)}{2}

154 = n(n - 3)

n^{2} - 3n - 154 = 0

n^{2} - 14n + 11n - 154 = 0

n(n - 14) + 11 (n - 14) = 0

(n - 14)(n + 11) = 0

n = -11, 14

Therefore No. of sides = 14

Video Explanation:

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

volume of a hollow cylinder = \pi\times h\times\left ( R^{2} - r^{2} \right )
=\frac{22}{7}\times 21\times (36 - 25) m³
=66 x 11 m³
=726 m³

Video Explanation: