Comprehensive Calculator Guide
A sphere's volume is 4/3 × π × radius³ and its surface area is 4 × π × radius². A football with an 11 cm radius has a volume of 5,575 cm³, about 5.6 litres, and a surface of 1,521 cm². Enter the radius in any unit to see both.
The formulas
V = 4/3 πr³ and A = 4πr², which is exactly four times the area of a circle with the same radius. The radius is hard to measure directly, so wrap a tape round the widest part and divide the circumference by 2π. A size 5 football is 68–70 cm round, so its radius is about 11 cm.
Because the radius is cubed, doubling it multiplies the volume by 8 but the area only by 4. That is why industrial tanks are spherical: a sphere holds the most volume for the least wall.
Hemispheres
A hemisphere holds half the volume, 2/3 πr³. Its curved surface is 2πr²; with a flat base add πr², giving 3πr² in total.
How to Use
- 01Enter the radius and its unit.
- 02From a diameter, halve it; from a circumference, divide by 6.2832.
- 03Choose units for volume, such as litres, and area.
- 04For a hemisphere, halve the volume.
Formula Used
Volume = 4/3 × π × r³ | Surface area = 4 × π × r²Practical Examples
Example 1: football
Radius 11 cm: 5,575 cm³ (about 5.6 L) and 1,521 cm².
Example 2: spherical tank
Radius 1 m: 4.19 m³, about 4,189 litres, and 12.57 m² of surface.
Example 3: radius 3 cm
Volume and area are both 113.1, in cm³ and cm², because 4/3 r³ = 4r² when r = 3.
Important Tips
- For a hollow shell, subtract the inner sphere's volume from the outer one.
Common Mistakes to Avoid
- Squaring the radius in the volume formula instead of cubing it.
- Using the diameter, which makes the volume eight times too big.
Frequently Asked Questions
- What is the formula for the volume of a sphere?
- V = 4/3 × π × r³, where r is the radius.
- How do I find the radius from the circumference?
- Divide by 2π: 69 cm gives about 11 cm.
- How do I find a hemisphere's volume?
- Halve the sphere's volume, or use 2/3 × π × r³.
- Why does doubling the radius multiply volume by 8?
- The radius is cubed, and 2³ = 8. Area, with the radius squared, grows by 4.