Surface Area And Volume Formulae

In our daily lives, we interact with objects of all shapes and sizes; most of these objects are made up of solid figures and have some area and volume. The surface area of an object is the total area covered by the surface of an object; by calculating the surface area, we can find out how much space an object takes. And the volume is the space occupied by an object in cubic units; the volume gives the amount of space an object takes up when contained. This article tells you about surface area and volume definition and formulae. 

Surface Area of Cuboid and Cube

After looking at surface area and volume, questions we can determine the formula of the surface area of cuboid and cube. The outer surface of the cuboid is made up of six rectangular sides; each of these sides is called the faces of a cuboid. The surface area of a cuboid can be determined by calculating the area of each face of the cuboid and then adding them together. Let us consider a cuboid with length l, breadth b, and height h, 

Calculating the surface area of each face of the cuboid,

Therefore, the total surface area of a cuboid is given by, 

A = 2(l.b + b.h + h.l)

A cube is a cuboid with equal sides; this means that all the faces of a cube make a square. Therefore, to calculate the surface area of a cube, we can add the surface area of all of its square sides,

The surface area of a square with a side a is given by,

Length x Length = a2,

Or, the surface area of a cube is given by,

A = 6a2

Surface Area of Right Circular Cylinder

Consider a sheet of paper with length l; now consider rolling this sheet to make a cylinder of height h. For this cylinder, the total surface area of the paper sheet will give the curved surface area of the cylinder, considering that the length of the paper is equal to the circumference of the cylinder.

We know 2.π.r gives the circumference of a circle;

The area of the curved surface of the cylinder is given as,

= area of the paper sheet (rectangular) = length x breadth,

= 2.π.r x h

Therefore, the area of the curved surface of a cylinder with a radius r is given by,

A = 2.π.r.h

When the top and bottom surface of the cylinder are also considered, we get the total surface area of a cylinder. The total surface area of a cylinder with a radius r is given by,

A = 2πr (r + h)

Surface Area of Right Circular Cone

The curved surface area of a cone with radius r, height h, and a slant height l is given by, 

The curved surface area of the cone,

A = ½  x (l x 2πr),

A = πrl

The total surface area of a cone with radius r, height h, and slant height l is given by,

The total surface area of the cone,

A = πrl + πr2

A = πr (l + r)

Surface Area of Sphere

The surface area of a sphere with a radius r is given by,

A = 4 x the area of a circle with radius r

A = 4 x πr2

Thus, the surface area of a sphere is given by,

A = 4πr2

The curved surface area of a hemisphere with a radius r is given by,

A = ½  x 4πr2

A = 2πr2

And the total surface area of a hemisphere is given by,

A = 3πr2

The Volume of a Cuboid and a Cube

 The volume of a cuboid with length l, height h, and breadth b is given by,

V = base area of cuboid x-height,

V = length x breadth x height

Therefore, the volume of a cuboid is given by,

V = l.b.h

Similarly, the volume of a cube with side a is given by,

V = a x a x a 

Therefore, the volume of a cube is,

V = a3

The Volume of a Cylinder

The volume of a cylinder with radius r and height h is given by, 

V = πr2h

The Volume of a Right Circular Cone

The volume of a right circular cone with radius r and height h is given by the following formula,

V = 13.(πr2h)

The Volume of a Sphere 

The volume of a sphere with radius r is given by the following formula,

V = 43. πr3

And the volume of a hemisphere with a radius r is given by,

V = 23.πr3 

Conclusion

The surface area and volume formulae of different solid shapes help determine the surface area and the volume of a particular object. This article tells us about the surface area and volume formula importance. When an object of any kind is placed in a space, it covers a certain area, the total area that the object covers on the plain is called the surface area. The volume of an object tells us the capacity of the object to hold a certain material or object. The area is measured in square units, while the volume is measured in cubic units.