# Volume and Surface Area Aptitude Question and Answer – Quantitative Aptitude

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:
1. When the radii are equal:
1. Ratio of volumes = ratio of heights.
2. Ratio of Curved Surface areas = ratio of heights.
3. Ratio of Volumes = (ratio of curved surface areas).
2. When height are equal
1. Ratio of volumes = (ratio of radii)2.
2. Ratio of curved surface areas = ratio of radii.
3. Ratio of volumes =(ratio of curved surface areas)2.
3. When volumes are equal
1. Ratio of radii = 2. Ratio of curved surface areas = 4. When curved surface areas are equal
1. Ratio of volumes = ratio of radii.
2. Ratio of volumes = inverse ratio of heights.
3. Ratio of radii = inverse ratio of heights.

Volume and Surface Area Aptitude Question and Answer With Detailed ExplanationQuantitative Aptitude

## Volume and Surface Area Aptitude

 Question 1
A Boat having a length 3m and breadth 2m is floating on a lake. The boat sinks by 1cm when a man gets on it. The Mass of the man is:
 A 12 Kg B 60 Kg C 72 Kg D 96 Kg
Question 1 Explanation:
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
A metallic sheet is of rectangular shape with dimensions 48m * 36m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8m, the volume of the box (in m3) is:
 A 4830 B 5120 C 6420 D 8960
Question 2 Explanation:
Explanation:
Volume of the box = Length * Breadth * Height
From the given,
Length = 48 * (2 * 8) (i.e., Two square formed side)
Length = 32m
Height = 8m, From the given
Therefore, Volume = 32 * 20 * 8 Volume of the box = 5120m3
 Question 3
The Curved surface area of a Cylindrical Pillar is 264m2 and its volume is 924m3. Find the ratio of its diameter to its height.
 A 3 : 7 B 7 : 3 C 6 : 7 D 7 : 6
Question 3 Explanation:
Explanation: Question 4
The Surface area of a cube is 600 cm2. The Length of its diagonal is
 A  B  C  D  Question 4 Explanation:
Explanation:
Surface area of cube = 6a2
600 = 6a2
a2 = 100 Question 5
The Slant height of a right circular cone is 10m and its height is 8m. Find the area of its curved surface.
 A  B  C  D  Question 5 Explanation:
Explanation: Question 6
A Cistern 6m long and 4m wide contains water up to a depth of 1m 25cm. The total area of the wet surface is:
 A 49m2 B 50m2 C 53.5m2 D 55m2
Question 6 Explanation:
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
50 men took a dip in a water tank 40m long and 20m broad on a religious day. If the average displacement of water by a man is 4m3, then the rise in the water level in the tank will be:
 A 20cm B 25cm C 35cm D 50cm
Question 7 Explanation:
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
The dimensions of a hall are 40m, 25m and 20m. If each person requires 200 cubic meters, find the number of persons who can be accommodated in the hall.
 A 150 B 140 C 120 D 100
Question 8 Explanation:
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
In a shower 10cm of Rain falls. What is the volume of water that falls on 1.5 hectares of ground?
 A 1500m3 B 1400m3 C 1200m3 D 1000m3
Question 9 Explanation:
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
A hollow sphere of internal and external diameters 4cm and 8cm respectively is melted to form a solid cylinder of base diameter 8cm. What is the height of the cylinder?
 A 4.5cm B 4.57cm C 4.67cm D 4.7cm
Question 10 Explanation: 