Area Calculation Aptitude Questions

Q1. A plot of land in the form of a rectangle has dimensions 240m x 180m. A draint 10m wide is dug all around it on the outside and the earth dug out is evenly spread over the plot increasing its surface level by 25cm. The depth of the drailent of

Outer length =(240 +20)m = 260m

Outer breadth =(180+20)m = 200m

Area of drailent =[(260 x 200) – (240 x 180)]m2

= (52000 - 43200)m2 = 8800m2

Let the depth of the drailent be x metres, then

8800 × x = 240 x 180 x 25/100

=> x = = 27/22 cm = 1.227m

Q2. A hall is a 15m long and 12m board. If the sum of the areas of the floor and the ceiling is equal to the areas of the 4 walls the volume of the hall is:

(lb +lb)= 2(l+b)x h

=> 2 x lb =2 (l+b)x h

=> lb =(l+b)x h => (15 +12)x h =(15 x 12)

=> h = 20/3 m

Volume =(l x b x h) =(15 x 12 x 20/3)m3 = 1200m3

Q3. The sum of the length breadth and depth of cuboid is 19cm and it’s diagonal is 5√5 cm it’s surface area is?

(l+b+h) = 19 and

=> (l+b+h) 2 =(19) 2 and (l2 +b2 +h2) = 125

=> (l2 +b2 +h2) + 2(lb +bh+lh) = 361 and

(l2 +b2 +h2) =125

=> 125 + 2(lb +bh+ lh) =361

=> 2(lb +bh+lh) =(361 -125) = 236

Surface area = 236 SQ.cm

Q4. The product of the area of three adjacent faces of a rectangular box is equal to

Product of area of 3 adjacent faces =(lb x bh x lh)

=(l2 b2 h2) =V2

Q5. The surface area of a (10cm x 4cm x3cm) brick is

Here l=10 cm , b =4 cm and h = 3 cm

Surface area = 2 (lb +bh +lh) = 2(10 x 4 + 4x3 + 10 x3) Sq.cm

=(2 x 82) Sq.cm = 164 Sq.cm

Q6. Water flows a tank 200 x 150m through a rectangular pipe 1.5 x 1.25m at the rate at 20kmph. In what time will be water rises by 2 meters?

Volume of water flown in the tank

=(200 x 150 x 2) Cu.m = 60000 Cu.m

Volume flown per hour

=(3/2 x 125/100 x 20 x 1000) Cu.m =37500Cu.m

Time taken = 60000/37500 hrs = 8/5 hrs

=(8/5 x 60)min = 96 min

Q7. The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103. Solving the two equations, we get: l = 63 and b = 40. Area = (l x b) = (63 x 40) m2 = 2520 m2.

Q8. What is the diameter of a wheel that makes 113 revolution to go 2km 26 decametre?

Distance = 2km 26 decametres =(2 x 1000)m +(26 x 10)m = 2260m

Distance covered in 1 revolution = 2260/113m = 20m

2R x 22/7 = 20 => 2R =(20x7/ 22) = 70/11 = 6 4/11 m

Q9. The radius of a circular wheel is 17.5m. How many revolutions will it make in travelling 11km?

Circumference of the wheel =(2 x 22/7 x 1.75)m =11m

Distance moved in 1 revolution = 11m

No.of revolutions made in covering 11km = 1000

Q10. The area of the base of a rectangular tank is 6500Sq.cm and the volume of water containing in it is 2-6 cubic meters. The depth of the water in the tank is

l x b =6500cm2 , l x b x d = 2.6cm3

=(2.6 x 100 x 100 x 100)cm3

Depth = 4m

Q10. The area of the base of a rectangular tank is 6500Sq.cm and the volume of water containing in it is 2-6 cubic meters. The depth of the water in the tank is

l x b =6500cm2 , l x b x d = 2.6cm3

=(2.6 x 100 x 100 x 100)cm3

Depth = 4m