Surface Area And Volume Definitions

We interact with different objects of different shapes; it is essential to know their surface area and volume definitions. The surface area and volume give us an idea about the shape and size of the object. The surface area mainly gives us information about the total area in the space covered by the object. The volume provides us with an idea about the capacity of an object to hold. The units used to measure the surface area and volume are m2 and m3, respectively. This article contains surface area and volume definition notes.

Surface Area

When it is placed in a space, the total space covered by an object is called the object’s surface area. A three-dimensional (having a definite length, breadth and height or depth) object, when placed in space, covers a particular area, the total area covered by the object is known as the object’s surface area.

The surface area of objects is further classified into three categories:

1.  Lateral surface area

2. Curved surface area

3. Total surface area

Lateral Surface Area

Lateral surface area is described as the total surface area of an object, excluding the surface areas of the top and bottom parts of the object.

In other words, the lateral surface area gives the surface area of the object’s cross-section. 

Curved Surface Area

Many solid objects like a cylinder and cones have a curved surface; the area of the object covered by the curved surface of such items is called the curved surface area.

Total Surface Area

The total surface area includes all the faces of the object; this gives us the total surface covered by the object in the physical space.

Surface Area Units

The surface area is always measured in square units. The unit used to measure the surface area of an object is m2; it is also called the S.I unit of surface area. However, in calculations, cm2, mm2 are also used.

Volume

The volume of an object is described as the total space occupied by the object and its capacity to hold a material or substance in it. In other words, the volume of an object gives us the total capacity of the object to hold in space.

• For example, a bucket of water with a volume of 5 litres can hold or occupy 5 litres of material.

• The volume of an object gives us the amount that an object can contain within.

Unit of Volume

The volume of solid objects is measured with cubic units. The standard unit of volume by the International System of Units (S.I) is m3. cm3, mm3 are other measuring units of volume.

Litres

The volume of liquids is measured in litres. 

The relationship between cm3 and litre is given by the following, 

1 litre = 1000 cm3,  

And, 1000 cm3 = (1000)(100X100X100) m3

1 litre = 0.001m3,

Or, 1 m3 = 1000 litres. 

Surface Area and Volume for Different Objects

So far, we have learned the surface area and volume definitions. Let us now see expressions for surface area and volume for different shapes,

Cuboid and Cube 

Consider a cuboid with breadth b, length l, and height h: 

Lateral surface area of cuboid = 2.(b.h + h.l),

Surface area of cuboid = 2.(l.b + b.h + h.l),

Volume of a cuboid = l. b. h.

And, for a cube with side a, 

Lateral surface area of a cube,  

AL = 4.a2

 The total surface area of the cube,

 A = 6.a2

 The volume of the cube, 

V= a3

Cylinder

Consider a cylinder having radius r, and height h,

The curved surface area of the cylinder,

AC = 2πrh,

The total surface area of the cylinder,

A = 2πr (h + r),

Volume of cylinder,

V = π.r2.h.

Cone

For a cone with base radius r, height h, and slant height l,

Curved surface area of cone,

Ac = π.r.l,

Total surface area of cone,

A = π.r.(r + l),

 Volume of cone,

V = 1/3.π.r2.h,

Consider a frustum of a cone with radius r1 and r2 and slant height l,

Curved surface area of the frustum of cone,

AC = π(r1 + r2).l

 Surface area of the frustum of cone,

A = π.l.(r1 + r2) + (πr1)2 + (πr2)2,

 Slant height of the frustum of cone,

l = √ [h2 + (r1 – r2)2]

Sphere and Hemisphere

For a sphere with a radius of r,

The surface area of the sphere,

A = 4.π.r2,

Volume of sphere,

V = 4/3.π.r3

 or a hemisphere with a radius of r, 

The surface area of the hemisphere,

A = 2.π.r2,

 The volume of the hemisphere,

V = 2/3.π.r3.

Conclusion

This article has defined surface area definitions importance. The surface area and volume definitions of different three-dimensional objects give us an idea about the space occupied by these objects. The area of objects is classified into the following three areas:

• Lateral surface area

• Circular surface area

• Total surface area. 

The surface area is measured in unit squares; the volume is measured in cubic units. 

The volume of an object gives an idea about the holding capacity of the object; the liquid materials are measured in litres,

1 litre = 0.001 m3.