Surface Areas and Volume - Definition, Formulas and Examples (2024)

Surface area and volume are calculated for any three-dimensional geometrical shape. The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object.

In geometry, there are different shapes and sizes such as sphere, cube, cuboid, cone, cylinder, etc. Each shape has its surface area as well as volume. But in the case of two-dimensional figures like square, circle, rectangle, triangle, etc., we can measure only the area covered by these figures and there is no volume available. Now, let us see the formulas of surface areas and volumes for different 3d-shapes.

Table of Contents:
  • Surface Area Definition
    • TSA
    • CSA
  • Volume Definition
  • Formulas
  • Solved Examples
  • Practice Questions
  • FAQs

What is Surface Area?

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area. It is also measured in square units.

Generally, Area can be of two types:

(i) Total Surface Area

(ii) Curved Surface Area/Lateral Surface Area

Total Surface Area

Total surface area refers to the area including the base(s) and the curved part. It is the total area covered by the surface of the object. If the shape has a curved surface and base, then the total area will be the sum of the two areas.

Curved Surface Area/Lateral Surface Area

Curved surface area refers to the area of only the curved part of the shape excluding its base(s). It is also referred to as lateral surface area for shapes such as a cylinder.

What is Volume?

The amount of space, measured in cubic units, that an object or substance occupies is called volume. Two-dimensional doesn’t have volume but has area only. For example, theVolume of the Circle cannot be found, though the Volume of the sphere can be. It is so because a sphere is a three-dimensional shape.

Learn more: Mathematics Grade 10

Surface Area and Volume Formulas

Below given is the table for calculating Surface area and Volume for the basic geometrical figures:

NamePerimeter Total Surface AreaCurved Surface Area/Lateral Surface AreaVolumeFigure
Square 4bb2—-—-Surface Areas and Volume - Definition, Formulas and Examples (3)
Rectangle2(w+h)w.h—-—-Surface Areas and Volume - Definition, Formulas and Examples (4)
Parallelogram2(a+b)b.h—-—-Surface Areas and Volume - Definition, Formulas and Examples (5)
Trapezoida+b+c+d1/2(a+b).h—-—-Surface Areas and Volume - Definition, Formulas and Examples (6)
Circle 2π rπr2—-—-Surface Areas and Volume - Definition, Formulas and Examples (7)
Ellipse2π√(a2 + b2)/2 π a.b—-—-Surface Areas and Volume - Definition, Formulas and Examples (8)
Trianglea+b+c1/2 * b * h—-—-Surface Areas and Volume - Definition, Formulas and Examples (9)
Cuboid4(l+b+h)2(lb+bh+hl)2h(l+b)l * b * hSurface Areas and Volume - Definition, Formulas and Examples (10)
Cube6a6a24a2a3Surface Areas and Volume - Definition, Formulas and Examples (11)
Cylinder—-2 πr(r+h)2πrhπr2 hSurface Areas and Volume - Definition, Formulas and Examples (12)
Cone—-πr(r+l)πr l1/3π r2 hSurface Areas and Volume - Definition, Formulas and Examples (13)
Sphere—-4π r24π r24/3π r3Surface Areas and Volume - Definition, Formulas and Examples (14)
Hemisphere—-3π r22π r22/3π r3Surface Areas and Volume - Definition, Formulas and Examples (15)

Related Articles

  • Surface Area and Volume Class 9
  • Surface Areas and Volumes Class 10 Notes

Also have a look on:

Surface Area Of A ConeVolume of a Cone
Surface Area Of CubeVolume Of A Cube
Surface Area of CuboidVolume Of Cuboid
Surface Area of a CylinderVolume of a Cylinder
Surface Area of a SphereVolume Of Sphere

Solved Examples

Example 1:

What is the surface area of a cuboid with length, width and height equal to 4.4 cm, 2.3 cm and 5 cm, respectively?

Solution:

Given, the dimensions of cuboid are:

length, l = 4.4 cm

width, w = 2.3 cm

height, h = 5 cm

Surface area of cuboid =2(wl+hl+hw)

= 2·(2.3 x 4.4 + 5 x 4.4 + 5 x 2.3)

= 87.24 square cm.

Example 2:

What is the volume of a cylinder whose base radii are 2.1 cm and height is 30 cm?

Solution:

Given,

Radius of bases, r = 2.1 cm

Height of cylinder = 30 cm

Volume of cylinder =πr2h =π·(2.1)2·30 ≈ 416.

Practice Questions on Surface Areas and Volumes

  1. Find the volume of a cube whose side length is 5 cm.
  2. Find the CSA of the hemisphere, if the radius is 7 cm.
  3. If the radius of the sphere is 4 cm, find its surface area.

Stay tuned to BYJU’S – The Learning App and download the app to explore all Maths-related concepts.

Frequently Asked Questions on Surface Area and Volume

Q1

What are the formulas for surface area and volume of cuboid?

Surface area of cuboid = 2(lb+bh+hl)
Volume = l × b × h
where l = length, b=breadth and h = height.

Q2

What is the total surface area of the cylinder?

The total surface area of the cylinder = 2 π r(r+h), where r is the radius of the circular base and h is the height of the cylinder.

Q3

How to calculate the volume of a cone-shaped object?

If r is the radius of the circular base of the cone-shaped object and h is the height, then the formula to find the volume of the cone is given by: V = 1/3π r2 h

Q4

What is the total surface area of the hemisphere?

The total surface area of the hemisphere is equal to the sum of half of the surface area of sphere and the area of its circular base.
Total surface area of hemisphere = 2 π r2+ π r2 = 3 π r2

Surface Areas and Volume - Definition, Formulas and Examples (2024)

FAQs

What are the formulas for surface area and volume? ›

ShapeSurface AreaVolume
CubeS A = 6 s i d e 2V o l u m e = s i d e 3
CuboidS A = 2 l w + w h + l h Where, length, width, heightV o l u m e = l e n g t h × w i d t h × h e i g h t
CylinderS A = 2 π r h + 2 π r 2 Where radius of the circular base HeightV o l u m e = π r 2 h
2 more rows

How to remember surface areas and volumes formulas? ›

One way to memorise these is to understand the concept by referring to NCERT solutions for class 9 maths chapter 13.
  1. For total surface area, think of it as the sum of the areas of all the surfaces. ...
  2. A tip for remembering volume is that volume is always the surface area of the base times the height of the object.
Nov 30, 2022

What is surface area and volume with example? ›

The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object. In geometry, there are different shapes and sizes such as sphere, cube, cuboid, cone, cylinder, etc.

How to solve surface area and volume problems easily? ›

Surface Area and Volume Formulas:
  1. Total surface area of a cuboid = 2[lb + bh + lh]
  2. Total surface area of a cube = 6(side) ...
  3. Lateral surface area of a cuboid = Area of walls of a room = 2(l + b) × h.
  4. Lateral surface area of a cube = 4a. ...
  5. Curved surface area of cylinder = 2πrh.
  6. Total surface area of a cylinder = 2πr(r + h)

What is the simple formula for surface area? ›

Variables:
Surface Area FormulaSurface Area Meaning
SA=2B+PhFind the area of each face. Add up all areas.
SA=B+12sPFind the area of each face. Add up all areas.
SA=2B+2πrhFind the area of the base, times 2, then add the areas to the areas of the rectangle, which is the circumference times the height.
2 more rows
Sep 17, 2020

What is the rule for surface area and volume? ›

For a cuboid (or cube), if we have the length 𝑙 , width 𝑤 , and height ℎ , then we can find the volume 𝑉 and surface area 𝑆 using the formulas 𝑉 = 𝑙 𝑤 ℎ , 𝑆 = 2 ( 𝑙 𝑤 + 𝑤 ℎ + ℎ 𝑙 ) .

How do you work out surface area and volume? ›

How to find the volume of a cube with the surface area? We can rearrange the equation for the surface area of a cube. SA = side of a cube x side of a cube x 6 sides. Since we know the length of the side of the cube, we can use that to calculate volume: Volume = length x width x height (of a side of a cube).

What is an example of a surface area? ›

The surface area of a polyhedron is the number of square units that covers all the faces of the polyhedron, without any gaps or overlaps. For example, if the faces of a cube each have an area of 9 cm2, then the surface area of the cube is 6⋅9, or 54 cm2.

What is an example of surface area and volume in everyday life? ›

How much water fills a swimming pool. How many cups a tea from a teapot. How much helium to fill a balloon. How much of the things you need to build anything, as anything can be broken down into many solid components.

What is the formula for all shapes? ›

Area Formula for Different Shapes
ShapeAreaTerms
Circleπ × r2r = radius of the circle
Triangle½ × b × hb = base h = height
Squarea2a = length of side
Rectanglel × wl = length w = width
3 more rows

How to calculate total surface area? ›

Finding the total surface area of an object means finding the surface area of each of the object's individual faces and then adding the measurements together. For instance, a cube is made of six squares. To find the total surface area of a cube, first find the area of one face of the cube and then multiply it by six.

What is the important formula for surface area and volume? ›

Surface Area and Volume Class 10 Formulas Examples

The volume of a cube = a3, where the length of the edge is 'a'. Using the formula for the surface area of a cuboid = 2(lb + bh + lh), where l, b, and h are length, breadth, and height respectively. Thus, the surface area of the resulting cuboid is 90 cm2.

What is the easiest way to find surface area? ›

In order to calculate the surface area:
  1. Calculate the area of each face.
  2. Add the area of each face together.
  3. Include the units.

How do you calculate surface area to volume? ›

To calculate SA/vol ratio: divide the surface area by the volume. For example, in the case of an organism with a surface area of 4 meters squared (m2) and a volume of 2 meters cubed (m3), the SA:Vol ratio is 2.

What is the formula of area? ›

The formula varies depending on the shape. For rectangles and squares, A = length x width. The area of a circle is A = 𝜋r2. Finally, the area of a triangle is A = ½ (base x height).

What is the formula for volume? ›

Formulas of Volume of Various Figures
ShapesVolume FormulaVariables
Rectangular Solid or CuboidV = l × w × hl = Length w = Width h = Height
CubeV = a3a = Length of edge or side
CylinderV = π r2hr = Radius of the circular base h = Height
PrismV = B × hB = Area of base, (B = side2 or length.breadth) h = Height
6 more rows

What is the formula for LxBxH? ›

The Volume of Cuboid

For any cuboid of length L, Breadth B, and height H, the volume 'V' is equal to LxBxH. The SI unit of this volume is a cubic meter (m^3).

Top Articles
Latest Posts
Recommended Articles
Article information

Author: Manual Maggio

Last Updated:

Views: 5934

Rating: 4.9 / 5 (49 voted)

Reviews: 88% of readers found this page helpful

Author information

Name: Manual Maggio

Birthday: 1998-01-20

Address: 359 Kelvin Stream, Lake Eldonview, MT 33517-1242

Phone: +577037762465

Job: Product Hospitality Supervisor

Hobby: Gardening, Web surfing, Video gaming, Amateur radio, Flag Football, Reading, Table tennis

Introduction: My name is Manual Maggio, I am a thankful, tender, adventurous, delightful, fantastic, proud, graceful person who loves writing and wants to share my knowledge and understanding with you.