Surface Area of Sphere Calculator | Free Online Surface Area of Sphere Calculator with Steps - BYJUS

# Surface Area of Sphere Calculator

The ‘surface area of sphere’ calculator is a free online tool that helps us calculate the surface area of a sphere as well as the radius of the sphere. Let us familiarize ourselves with the calculator....Read MoreRead Less

## Online Surface Area of Sphere Calculator

### How to use the ‘Surface Area of Sphere Calculator’?

Follow the steps given here to use the surface area of sphere calculator:

Step 1: Enter the known measure (either the radius or the surface area of the sphere) into the respective input box and the unknown measure will be calculated.

Step 2: Select the appropriate units for the input and output.

Step 3: You can also select the desired value of ‘pi’ from the dropdown box. The value for ‘pi’  can either be 3.14 or $$\frac{22}{7}$$.

Step 4: Click on the ‘Solve’ button to obtain the result.

Step 5: Click on the ‘Show Steps’ button to know the stepwise solution to find the missing measure.

Step 6: Click on the  button to enter new inputs and start again.

Step 7: Click on the ‘Example’ button to play with different random input values.

Step 8: Click on the ‘Explore’ button to visualize the transition of a sphere into a cylinder and then into a rectangle by using the slider provided.

### What is the Surface Area of a Sphere?

A sphere is a three-dimensional round figure. The points on the surface of the sphere are equidistant from a fixed point called the center of the sphere. The line segment that joins the center to a point on the surface of the sphere is called the radius. Surface area of a sphere is the area of its outer surface.

### Relationship Between the Surface Area of a Sphere and the Lateral Surface Area of a Cylinder

Let’s consider a sphere of radius r

The surface area of the sphere, S = $$4\pi r^2$$

Now, consider a cylinder with radius r and height 2r.

The lateral surface area of the cylinder = 2$$\pi$$rh

= 2$$\pi$$r . 2r

= 4$$\pi r^2$$

Therefore, we can conclude that the surface area of a sphere is equal to the lateral surface area of a cylinder of the same radius and whose height is twice the radius.

Let’s go one step further.

Let’s take the same cylinder, cut along its height and then unravel it, such that a rectangle is formed. As a result, the rectangle will have the same height as the cylinder which is, 2r and the width of the rectangle will be equal to the circumference of the base of the cylinder, which is 2$$\pi$$r.

Area of rectangle = height $$\times$$ width

= 2r$$\times 2\pi r$$

= 4$$\pi r^2$$

Therefore, the area of the rectangle thus formed is equal to the surface area of the sphere as well as the lateral surface area of the cylinder.

### Formulas used in the ‘Surface Area of Sphere Calculator’

The surface area of a sphere of radius r is calculated according to the formula:

Surface Area, S = $$4\pi r^2$$

On rearranging the formula,

The radius of the sphere can be calculated according to the formula:

Radius, r = $$\sqrt{\frac{S}{4\pi}}$$

### Solved Examples

Example 1:  Find the surface area of the sphere given in the image. Take the value of pi as, $$\pi$$ = 3.14

Solution:

Surface area of sphere, S = 4$$\pi r^2$$

S = 4 $$\times$$ 3.14 $$\times 8^2$$

S = 803.84 $$in^2$$

Hence, the surface area of the sphere is 803.84 square inches.

Example 2: Find the radius of a sphere that has a surface area of 250 $$mm^2$$. Take the value of pi as, $$\pi=\frac{22}{7}$$

Solution :

Surface area of sphere, S = 4$$\pi r^2$$

Therefore, r = $$\sqrt{\frac{S}{4\pi}}$$

r = $$\sqrt{\frac{250}{4 \times \frac{22}{7}}}$$

r = 4.459 mm

Hence, the radius of the sphere is 4.459 millimeters.

Example 3: Find the radius of a soccer ball, if its surface area is 800 square centimeters. Use 3.14 as the value of .

Solution:

Surface area of sphere, S = 4$$\pi r^2$$

Therefore, r = $$\sqrt{\frac{S}{4\pi}}$$

r = $$\sqrt{\frac{800}{4 \times 3.14}}$$

r = 7.981 centimeters

So, the radius of the soccer ball is 7.981 centimeters.