Question

Volume of a sphere

Tr³, where r is the radius.
Пр
The bouncy ball below is a sphere with a volume of 4800 mm
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Calculate its radius, r.
If your answer is a decimal, give it to 2 d.p.

Answer 1

To calculate the radius of a sphere with a known volume, use the formula V = (4/3)πr³ and solve for r. For a sphere volume of 4800 mm³, the radius is approximately 10.61 mm when rounded to two decimal places.

Step-by-step explanation:

Calculating the Radius of a Sphere

To find the radius r of a sphere when given the volume V, we use the formula for the volume of a sphere, which is V = (4/3)πr³. We can rearrange this formula to solve for r when given a specific volume. In this case, the student asked for the radius of a sphere with a volume of 4800 mm³.

Step-by-step solution:

1. 
   
3. Start with the volume formula: V = (4/3)πr³.
4. 
   
6. Plug in the known volume: 4800 mm³ = (4/3)πr³.
7. 
   
9. Rearrange to solve for r³: r³ = (4800 mm³) / ((4/3)π).
10. 
    
12. Calculate r³: r³ = 4800/(4.18879) [using π ≈ 3.14159].
13. 
    
15. Take the cube root of both sides to solve for r.

After performing these calculations, we find that the radius r is approximately r = 10.61 mm (to two decimal places).

It is important to note that the volume of a sphere is given by the formula V = (4/3)πr³, not 4² or 4³/3, as these represent surface area and volume of a cube, respectively.