# Baseball and string activity to find the surface area of a sphere

From Karnataka Open Educational Resources

### Objectives

### Estimated Time

1 hour

### Prerequisites/Instructions, prior preparations, if any

Circles should have been covered.

### Materials/ Resources needed

Non digital: Baseballs, string, marker pens, scale, scissors and chart paper

Digital: Computer and projector

This activity has been taken from the website ehow.com

### Process (How to do the activity)

- Process:

- Divide the class into groups and give each group a baseball and string.
- Ask the students to lay flat the string around the widest part of the baseball and mark.
- The meaured length would be the circumference.
- The measurement will be divided by pi to find the diameter (Remember: circumference/diameter = pi).
- The diameter divided by 2 would be the radius. Note down the radius.
- Now take a long piece of string and carefully wind it around the entire surface of the ball taking care not to overlap.Cut and discard the extra string.
- Next unwind the string,measure it using a measuring tape. This measure would be teh surface area of the sphere.

To understand the formula **Failed to parse (syntax error): {\displaystyle 4πr^2}**
for deriving surface area of a sphere :

- Consider the length of string obtained from step 7 , divide it into exactly 4 equal parts.
- Make a circle with each part. Measure the radii.
*( Hint: Can draw circle of radius from step 5 and lay the string around it)* - Observe that 4 circles would be equal and the radii in all 4 cases would be the same as the radius of sphere (derived initially by measuring circumference).
- The length of string covering the entire surface area of the sphere has been formed into 4 circles of equal radius.
- The area of 1 circle is
**Failed to parse (syntax error): {\displaystyle πr^2}** - The area of 4 such circles would be 4 times the area of such circle.
- Hence teh area of a sphere would be
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 4πr^2}**

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