Volume and Surface Area Aptitude Question and Answer – Formulas
Square
Area = S2
Perimeter = 4s
s = length of the sides, d = length of diagonal.
Rectangle
Area = base * height = b * h
Perimeter = 2 (b + h)
Triangle
Area = (1/2) * base * height
Perimeter = x + y + z (Summation of three sides of a triangle)
Rhombus
Area = (1/2) * Product of the diagonals between the sides * sine of the angle between the sides.
Perimeter = 4 * side (any side)
Diagonal = 2 * area / diagonal
Parallelogram
Area = Product of any two sides * sine of the included angle
Perimeter = 2 (a + b) (a and b are the two adjacent sides)
Trapezium
Area = (1 / 2) * Sum of the parallel sides * height
Cuboid
Let length = l, breadth = b, and height = h
- Volume of cuboid = (l * b * h) cubic units
- Whole surface area of cuboid = 2(lb + bh + hl) sq.units
- Diagonal of cuboid =
units.
Cube
Let each edge of a cube = “a” units.
- Volume of the cube = a3 cubic units.
- Whole Surface area of cube = (6a2) sq. units.
- Diagonal of the cube =
units.
Cylinder
Let the radius of the base of a cylinder be r units and height of the cylinder be h units.
- Volume of the cylinder = (πr2h) cubic units.
- Curved Surface area of the cylinder = (2πrh) sq.units
- Total Surface area of the cylinder = (2πrh + 2πr2) sq.units
Sphere
Let r be the radius of the sphere.
- Volume of the sphere =
cubic units.
- Surface area of the sphere =
sq. units.
- Volume of hemisphere =
cubic units.
- Curved Surface area of the hemisphere = (2πr2) sq. units.
- Whole Surface area of the hemisphere = (3πr2) sq. units.
Right Circular Cone:
Let r be the radius of the base, h is the height, and I is the slant height of the cone.
- Slant height I =
- Volume of the cone =
cubic units.
- Curved surface area of the cone = (πrI) sq. units =
sq. units.
- Total Surface area of the cone = (πrI + πr2) = πr(I + r) sq. units.
Frustum of a right circular cone:
Let the radius of the base of the frustum = R, the radius of top = r, height = h and slant height = l units.
- slant height, l =
unit.
- Curved surface area = π (r + R) l sq. units.
- Total Surface area = π {(r + R) l + r2 + R2} sq. units.
- Volume = (πh / 3) (r2 + R2 + rR) cubic units.
Volume and Surface Area Aptitude Quick Method
For a Closed Wodden box:
- Capacity = (external length – 2 * thickness) * (external breadth – 2 * thickness) * (external height – 2 * thickness).
- Volume of Material = External Volume – Capacity.
- Weight of Wood = Volume of Wood * Density of wood.
Problems Involving Ratios:
- Two Spheres
- (Ratio of radii)2 = ratio of surface areas.
- Ratio of Volumes = (ratio of radii)3.
- (Ratio of surface areas)3 = (ratio of volume)2 .
- Two Cylinders:
- When the radii are equal:
- Ratio of volumes = ratio of heights.
- Ratio of Curved Surface areas = ratio of heights.
- Ratio of Volumes = (ratio of curved surface areas).
- When height are equal
- Ratio of volumes = (ratio of radii)2.
- Ratio of curved surface areas = ratio of radii.
- Ratio of volumes =(ratio of curved surface areas)2.
- When volumes are equal
- Ratio of radii =
- Ratio of curved surface areas =
- Ratio of radii =
- When curved surface areas are equal
- Ratio of volumes = ratio of radii.
- Ratio of volumes = inverse ratio of heights.
- Ratio of radii = inverse ratio of heights.
- When the radii are equal:
Volume and Surface Area Aptitude Question and Answer With Detailed Explanation – Quantitative Aptitude
Volume and Surface Area Aptitude
Question 1 |
12 Kg | |
60 Kg | |
72 Kg | |
96 Kg |
Explanation:
Volume of Water displaced = ( 3 * 2 * 0.01)m3
=0.06m3
Therefore, Mass of man= Volume of water displaced * Density of water
=(0.06 * 1000)kg
Mass of man = 60kg
Question 2 |
4830 | |
5120 | |
6420 | |
8960 |
Explanation:
Volume of the box = Length * Breadth * Height
From the given,
Length = 48 * (2 * 8) (i.e., Two square formed side)
Length = 32m
Breadth = 36 - (2*8)
Breadth = 20m
Height = 8m, From the given
Therefore, Volume = 32 * 20 * 8 Volume of the box = 5120m3
Question 3 |
3 : 7 | |
7 : 3 | |
6 : 7 | |
7 : 6 |
Explanation:

Question 4 |
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Explanation:
Surface area of cube = 6a2
600 = 6a2
a2 = 100

Question 5 |
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Explanation:

Question 6 |
49m2 | |
50m2 | |
53.5m2 | |
55m2 |
Explanation:
Area of the Wet Surface = [2 * (lb + bh + lh) - lb]
= 2* (bh + lh) + lb
=[2* (4 * 1.25 + 6 * 1.25) + (6 * 4)]m2
= 49m2
Question 7 |
20cm | |
25cm | |
35cm | |
50cm |
Explanation:
Total Volume of water displaced = (4 * 50)m3 = 200m3
Therefore, Rise in water level = (200 / (40*20))m = 0.25m
The rise in the water level in the tank = 25cm
Question 8 |
150 | |
140 | |
120 | |
100 |
Explanation:
Length of the hall = 40m
Breadth of the hall = 25m
Height of the Hall = 20m
Volume of the hall = L * B * H
= 40 * 25 * 20 = 20,000m3
Space Occupied by each person = 200m3
No. of Person that can accommodate in the hall = (Volume of the hall / Space Occupied by one person)
=(20000/200)
No. of Person that can accommodate in the hall = 100Persons
Question 9 |
1500m3 | |
1400m3 | |
1200m3 | |
1000m3 |
Explanation:
1 Hectare = 10,000m2
1.5 Hectare = 1.5 * 10,000 = 15,000m2
Depth = 10cm of rainfall = (10/100)
Therefore, Volume of water = Area * Depth
=15,000 * (10/100)
Volume of water = 1500m3
Question 10 |
4.5cm | |
4.57cm | |
4.67cm | |
4.7cm |
Explanation:
