Volume and Surface Area – Aptitude Question and Answer

Volume and Surface area topics are very crucial topics for any exam that has Quantitative Aptitude section in their exam pattern. One such National exam is SSC CGL, Every year you can witness at least one question from this topic and as we all know, in any government exam, even a single mark can make a huge difference in ranking or clearing the cut-off. 

In this article, we will cover everything you need to know about calculating the volume and surface area of various shapes and objects, along with tips and tricks to solve related questions quickly and accurately. With our comprehensive guide, you’ll be well on your way to acing the quantitative section of SSC CGL! Whether you are a beginner or an advanced learner, this article will help you to enhance your understanding of the topic and improve your performance in the exam. So, let’s dive into the world of Volume and Surface Area! 

Volume and Surface Area

Understanding the Basics of Volume and Surface Area in Quantitative Aptitude

What is surface area? 

Surface Area is a term used to describe how much space a 2D flat surface or a 3D object’s outside surface occupies. Usually, it is expressed in terms of square measurements like acres, square meters, or square feet.

There are two types of surface areas for any 3D object:

1. Curved Surface Area (CSA) or Lateral Surface Area: It only includes the curved area of the shape
2. Total Surface Area (TSA): TSA includes the entire surface area, i.e., the curved surface area + the area of the base(s). 

What is Volume? 

Volume is the amount of space occupied by an object in three-dimensional space. It is measured in units such as cubic meters (m³), cubic centimeters (cm³), or liters (L). In simpler terms, it is the amount of space that an object occupies.

Formulas of Volume and Surface Area 

The table given below contains different shapes, types, dimensions, perimeter, Total Surface Area, Curved Surface Area/Lateral Surface Area, Volume, and their physical representation : 

Name of the Shape	Type	Dimensions	Perimeter	Curved Surface Area	Total Surface Area	Volume	Shape
Triangle	2 D	3 Sides	a+b+c	—	1/2 h.b	—
Square	2 D	4 Equal Side	4b	—	b2	—
Rectangle	2 D	Length and Breadth	2(h+w)	—	h.w	—
Trapezium	2 D	4 Different Sides, Perpendicular	a+b+c+d	—	1/2(a+b).h	—
Parallelogram	2 D	Two Sides, Perpendicular	2(a+b)	—	b.h	—
Circle	2 D	Radius	2πr	—	πr2	—
Eclipse	2 D	2 Axis	2π√(a2 + b2)/2	—	πa.b
Cube	3 D	Length = Breadth = Height	6a	4a2	6a2	a3
Cuboid	3 D	Length, Breadth and Height	4(l+b+h)	2(lb+lh+hb)	2h(l+b)	l.b.h
Cylinder	3 D	Radius of the Base, Height	2πr(r+h)	2πrh	πr2h
Sphere	3 D	Radius	—	4πr2	4πr2	4πr3/3
Hemisphere	3 D	Radius		4πr2	3πr2	2πr3/3
Right Circular Cone	3 D	Slant Height & Radius of the Base		πrl	πr(r+l)	1/3 πr2h

How to Calculate Volume and Surface Area: Step-by-Step Guide 

Step 1: Find the shape of the object, such as cube, cuboid, cone, sphere, cylinder, etc

Step 2: Measure all the sides of the object i.e., length, breadth, and height in one S.I. unit

Step 3: Use the right formula as per the shape of the object to calculate the volume or surface area of the object. Take down the formula from the above table.

Step 4: Don’t forget to change all the dimensions in the same unit, i.e. all the sides in meters or in cm or in km

Step 5: Simply the formula and check all your calculations.

Repeat these steps for any other shape whose volume and surface area you need to calculate.

Tips and Tricks to Master Volume and Surface Area Questions in Competitive Exams

Before are some key pointers to master volume and surface area questions.

1. Practice Regularly
2. Try to visualize the shapes
3. Pay attention to units
4. Memorise the formulas
5. Break down Complex shapes
6. Check your answer
7. Labeling the Diagram
8. Time management
9. Analyze past papers
10. Seek help: Whenever you are having trouble understanding a concept or question, ask your teacher, tutor, or peers for help. It is important to clear your doubts to avoid confusion and build your confidence in solving these types of questions.

Practice Questions on Volume and Surface Area Aptitude Questions and Answers

We are providing you with a few concept-based volume and surface area questions for the SSC CGl exam with detailed solutions.

Question 1. 

Ram has a cube-shaped dice with a total diagonal length of 16 cm. What is the total length of its edges?

Solution:

Let the length of the diagonal be x

4x=16

x= 4 = √3 a, where a is the side length of the cube

Total Length of its Edges = 12a = 16 √3 cm 

Question 2. 

A solid spherical ball can displace 5 cubic meters of water. What will the increase in water level be if 40 such balls are submerged in a tank at once?  Dimensions of the tank are 40 m X 20 m X 10 m.

Solution:

Total Displaced water = 5* 40 m³ = Length of the Tank * Breadth * Increase in the Water Level 

5*40 = 40 * 20 * H

H= 5/20 m = 25 cm

Question 3.

If a cone’s height and base radius are both increased by 100%, the cone’s volume will change by what percentage?

Solution:

Volume of the cone=v = 1/3 πr²h 

New Radius = R=r+r=2r

New Height= H= h+h=2h

New Volume =V= 1/3πR²H = 1/3 π(2r)²(2h) = 8 v

Question 4.

Which of the following statements is true if the areas of a circle, a square, and an equilateral triangle are C, S, and T, respectively, and their perimeters are the same?

a) C=S=T
b) S<C<T
c) C>S>T
d) C<S<T

Solution:

Perimeter of Circle= Perimeter of Square= Perimeter of Triangle

 2πr= 4a=3s   [where r is the radius of the circle, a is the side of the square, and s is the side length of the triangle]

r= 2a/π , r = 1.5s  ——-(i)

Area of the Circle = πr²

Area of the Square = a²

Area of the Triangle = 1/2.s. h, [h= (s√3)/2]

Using (i)

C : S : T =  πr²  : (πr/2)²  : 1/2 . (r/1.5). [(r/1.5)√3)/2]

on Solving,

C > S> T

Option C is the correct Answer

Question 5.

Find the height of a parallelogram if its base and area are  30cm and 540 sq cm, respectively.

Solution:

Area = Base × Height

Height = Area/ Base = 540/30 = 18 cm

Question 6.

The diameter of the front wheel of an engine is 2r cm and that of the rear wheel is 2R cm. To cover the same distance, find the number of times the rear wheel will revolve when the front wheel revolves times.

Solution:

Circumference of front wheel = 2πr,           r= radius of the front wheel

Distance covered by the front wheel when it revolves n times = (n x 2πr) cm 

Circumference of rear wheel = 2πR,          R = radius of the rear wheel

Suppose, the rear wheel revolves ‘b’ times;

Distance covered by the rear wheel when it revolves m times = (b x 2πR) cm

The distance covered is the same;

(a x 2πr) = (b x 2πR)

b = ar/R

Rear wheel revolves ‘ar/R’ times.

Question 7.

Two circles that touch on their outsides have a combined area of 130 sq cm, and their centers are separated by 14 cm. Find the diameters of both circles.

Solution:

Let the radius of the two circles be a and b cm

The circles touch each other externally.

So, the distance between their centers =a+b

a+b=14 ………………. (1)

Sum of their areas =πa²+πb² =130π

=> a²+b² =130 …………………(2)

From equation (1),

b=14−a  …………. (3)

From (2) and (3),

a²+(14−a)²=130

On solving quadratic equation, a=3,11

If a=3,  then b=14−3=11

If a=11,  then  b=14−11=3

So, the radius of the two circles are 3 and 11 cm

And their diameters are 6 and 22 cm.

Question 8.

A triangle has an area of 34 sq cm and an inradius of 4 cm. Find the perimeter of the triangle.

Solution:

Area of the Triangle = Inradius * Semi Perimeter of the Triangle = Inradius * Perimeter/2 

Perimeter = 2 * Area of the Triangle / Inradius 

Perimeter = 17 cm

You can also read, 

Surface Area Formulas Area of Triangle Area of Square Area of Circle Area of Rectangle Area of Trapezium Area of Parallelogram  Area of Cuboid Area of Cube Area of Sphere Area of Hemisphere Area of a Cone Perimeter and Surface Area

FAQ’s on Volume and Surface Area

How to calculate the volume of a cylinder?

You can calculate the volume of the cylinder by using the formula πr²h, where r is the radius of the base and h is the height of the cylinder. 

How to calculate the volume of a sphere? 

The formula for the volume of a sphere is 4πr³/3, where r is the radius of the sphere, similarly, the volume of the hemisphere can be calculated by dividing the volume of the sphere by 2, i.e. 2πr³/3.

What is the total surface area of the right circular cone?

The total surface area of the Right Circular Cone = Curved Surface Area + Area of the Base = πrl + πr² = πr (r+l).

What is the volume of the tank?

The tank could be of cube, cuboid, or cylindrical shape. One should not assume the shape of the tank and calculate the volume. The shape of the tank will be clearly mentioned in the exam either directly or by mentioning the dimensions. 

How to calculate the volume of the cylinder from the surface area of the base and height?

Volume of the Cylinder= Surface Area of the Base * Height of the Cylinder