Area of Sphere

Define Sphere

 

Sphere is the one type of three dimensional geometrical objects.Surface area is an total amount of outer area of a three dimensional sphere.

A sphere is a perfectly round geometrical object. It is a three dimensional shape. The volume and surface area of sphere can be calculated easily if radius is given. The volume of sphere is expressed in terms of cubic unit and area of sphere is expressed in terms of square unit. In this article we are going to see about surface area and volume of sphere with example problems. 

 

Formula to find surface area and volume sphere:

 

Surface area of the sphere (A) = 4 π rsquare unit

A- Surface area.

 r- Radius

Volume of a sphere (v) = `4/3`  π r cubic unit

    V-volume

     r- Radius

 

Problems to find volume surface area sphere:

 

   Ex 1:  The sphere has radius of 3.5cm. Find the surface area and volume of sphere.

Sol:

Given:

      Radius (r) = 3.5 cm

Formula:

Surface area of the sphere (A) = 4 π rsquare unit

A- Surface area.

 r- Radius

            Substitute the r value in the formula and simplify,

                                                                = 4 x π x 3.52

                                                               =4 x π x 12.25

            Surface area of the sphere (A) = 153.86 cm2

Volume of the sphere (v) = `4/3`  π r cubic unit

            V-volume

            r- Radius

            Substitute the r value in the formula and simplify,

                                                            = `4/3`  x π x (3.5)3

                                                            =`4/3` x 3.14 x 42.875

            Volume of the sphere (v)       = 179.503 cm3 

Ex 2:  The sphere has radius of 7m. Find the surface area and volume of sphere.

Sol:

Given:

      Radius (r) = 7m

Formula:

Surface area of the sphere (A) = 4 π rsquare unit

A- Surface area.

 r- Radius

            Substitute the r value in the formula and simplify,

                                                                = 4 x π x 72

                                                               =4 x π x 49

            Surface area of the sphere (A) = 615.44m2

Volume of the sphere (v) = `4/3`  π r cubic unit

            V-volume

            r- Radius

            Substitute the r value in the formula and simplify,

                                                            =  `4/3` x π x (7)3

                                                            =`4/3` x 3.14 x 343

            Volume of the sphere (v)       = 1436.02 m3

Ex 3: Find the surface area of a sphere whose radius 4cm?

Sol:

Given:

r = 4cm

Surface area of cone = 4πr2

                                       = 4 ×3.14× 42 

                                       = 4 ×3.14× 16

                                       = 200.96cm2

Ex 4: Find the surface area of a sphere whose radius 6cm?

Sol:

Given:

r = 6cm

Surface area of cone = 4πr2

                                       = 4 ×3.14× 62 

                                       = 4 ×3.14× 36

                                       = 452cm2

Practice problems:

1. The sphere has radius of 5.7m. Find the surface area and volume of sphere.

Ans:

Surface area (A) = 408.28137 m2

Volume          (V) = 775.7346 m3

2. The sphere has radius of 6.5cm. Find the surface area and volume of sphere.

Ans:

Surface area (A) = 530.92 cm2

Volume          (V) = 1150.3466 cm3

3. The sphere has radius of 9.3cm. Find the surface area and volume of sphere.

Ans:

Surface area (A) = 1086.8654 cm2

Volume          (V) = 3369.2827 cm3

3) Find the surface area of a sphere whose radius 7cm?

Ans:  615cm2

4) Find the surface area of a sphere whose radius 9m?

Ans: 1017m2