REPEATED QUESTIONS ON GEOMETRY WITH ANSWERS
REPEATED QUESTIONS ON GEOMETRY WITH ANSWERS
1. A conical tent is to accommodate 10 persons. Each person must have 6 sq.meter space to sit and 30 cubic meters 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 meters 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 the 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 the 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 that 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
Explanation:X must be the center of the circle and 32 points are on the circumference. So Option A is correct
Number of diagonals of a regular polygon =
n(n−3)/2
So for a polygon of 32 sides, the Number of diagonals = 464. Now the minimum distance between any two points = 2πr/32=11r/56
Now the total length of all the distances from 32 points = 2πr + Sum of the lengths of all the 464 diagonals.
Some of the lengths of x to all the 32 points = 32 radius = 32r
But the 464 diagonals have 16 diameters connecting 2 opposite points connecting via center. So Sum of the lengths of distances from point to point is clearly greater than the sum of the length from x to all 32 points. 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
Explanation:
Let the radius of the pool be r. Then the 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 the 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
Explanation: Let the side of the 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 the area of the square = 1/2(2/2)=2
The ratio of the areas of an equilateral triangle and square = √3/4 : 2 ⇒√3:8
THANK YOU & ALL THE BEST
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