TCS Questions on Geometry with Answers – 1

1. A conical tent is to accommodate 10 persons.  Each person must have 6 sq.meter space to sit and 30 cubic meter of air to breathe.  What will be the height of the cone?
a. 150m
b. 37.5 m
c. 15 m
d. 75 m
Answer: c
Explanation:
Each person needs 6 sq meter of space. So
πr2=6×10=60
Total volume of the tent = 30 × 10 = 300
So 1/3(πr2)h=300 ⇒ 1/3×60×h=300
h = 15 m

2.The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and height are halved, while the length is doubled. Then the total area of the 4 walls of the room will be decreased by
a. 30%
b. 18.75%
c. 15%
d. 13.6%
Answer:a
Explaination: Given l:b:h=3:2:1
let h=10, b = 20, and l = 30
area = 2(l+b)h
area= 2*(3x+2x)*x = 2(30+20)10=1000
Now after those adjustments in the measurements,
l=60, b=10, h=5
area= 2(l+b)h = 2(60+10)5=700
Percentage decrease=
(1000−700)/1000 ×1000 =30 %

3.Arun makes a popular brand of ice cream in a rectangular shaped bar 6cm long, 5cm wide and 2cm thick. To cut costs, the company had decided to reduce the volume of the bar by 19%. The thickness will remain same, but the length and width will be decreased by some percentage. The new width will be,
a. 5.5
b. 4.5
c. 7.5
d. 6.5
Answer:b
Explaination:
Volume =l×b×h = 6×5×2 = 60 cm3
Now volume is reduced by 19%.
Therefore, new volume = (100−19)/100×60=48.6
Now, thickness remains same and let length and breadth be reduced to x%
so, new volume: (x/100*6)(x/100*5)*2 =48.6
Solving we get x =90
thus length and width is reduced by 10%
New width = 5-(10% of 5)=4.5

4.11. There is a plane contains 32 points.all the 32 points have equal distance from point x. which of the following is true .
a. all 32 points lie in circle
b. the distance from x to all 32 points is less than the distance between each other
c. both a and b
d. none of these
Answer: Option 3
Explaination:X must be the center of the circle and 32 points are on the circumference. So Option A is correct
Number of diagnols of a regular polygon =
n(n−3)/2
So for a polygon of 32 sides, Number of diagonals = 464. Now the minimum distance between any two points = 2πr/32=11r/56
Now total length of all the distances from 32 points = 2πr + Sum of the lengths of all the 464 diagonals.
Sum of the lengths of x to all the 32 points = 32 radius = 32r
But the 464 diagnols have 16 diameters connecting 2 oposite points connecting via center. So Sum of the lengths of distances from point to point is clearly greater than sum of the length from x to all 32 ponts. Option B is correct
Correct Option 3

5.A circular swimming pool is surrounded by a concrete wall 4 feet wide.if the area of the wall is 11/25 of the area of the pool, then the radius of the pool in feet is?
a.10
b.20
c.15
d.17
Answer:b
Explaination:
Let the radius of the pool be r. Then area of the wall and pool =
π(r+4)2
Area of the pool = π(r)2
Area of the wall = π(r+4)2−π(r)2
Given π(r+4)2−π(r)2 = 11/25(πr2)
r2+8r+16−r2=11/25r2
11r2−200r−400=0
Solving r = 20

6.The diagonal of a square is twice the side of equilateral triangle then the ratio of Area of the Triangle to the Area of Square is?
a.√3:8
b.√3:4
c.√2:8
d.√2:3
Answer:a
Explaination:Let the side of equilateral triangle = 1 unit.
We know that area of an equilateral triangle = √3/4a2
As side = 1 unit area of the equilateral triangle = √3/4
Now Diagonal of the square = 2 (side of the equilateral triangle) = 2
We know that area of the square = 1/2D2
where D = diagonal
So area of the square = 1/2(2/2)=2
Ratio of the areas of equilateral triangle and square = √3/4 : 2 ⇒√3:8