TCS Ninja Geometry Questions Part 1

1 dm = 0.1 m

Now ,

Dimensions of the ground :

Length = AB = 19m 2.5 DM

AB = 19.25 m

Breadth = BC = 12m 5dm

BC = 12.5 m

If 2 m wide path goes across to the

center of the opposite sides .

width of the path = w = 2 m

From the figure ;

area of the path( A ) = area of EFGH + area of

PQRS - area of Square KLMN

A = EF × w + QR × w - w²

= AB × w + BC × w - w²

= 19.25 × 2 + 12.5 × 2 - 2²

= 38.5 + 25 - 4

= 63.5 - 4

A = 59.5 m²

Therefore ,

Area of the path = A = 59.5 m²

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:

Area = \frac{1}{2}\times 8\times 10 = 40 cm^{2}

Video Explanation:

Range of sin function is -1 to 1

Length of plot =112m, Breadth =78m

Area of plot= 112\times 78= 8736 m^{2}

Now After forming the path

The length of remaining plot l=112−2(2.5)=108m

Breadth b=78−2(2.5)=73m

Area of remaining plot = 108\times 73 = 7811  m^{2}

Area of path =8736−7811=925m^{2}

Video Explanation:

Plate is in shape of cylinder.

Height = 1 cm
radius of sphere = 3 cm
Volume of sphere = \frac{4}{3} \pi r^{3}
= \frac{4}{3} \times 3.14 \times 3^{3}
= 113.04
Volume of plate = \pi r^{2} h
= 3.14 \times r^{2}\times 1
= 3.14 \times r^{2}
Since we are given that the plate is made up by recasting the sphere
So, volume will remain same .
So,3.14 \times r^{2} =113.04
r^{2}=\frac{113.04}{3.14}
r^{2}=36
r=6
Thus the radius of circular plate is 6 cm

Video Explanation:

Solution:

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

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

Video Explanation: