## How many onions should I cut?## 1 large onion equals 8 small onesSeptember 1, 2019, |
Often we can't imagine how many small onions we should cut instead of the big one.
Luckily, we can calculate this using a simple three-dimensional sphere volume formula.
Suppose we have a large onion that has each of 3 dimensions twice the size of the small one.
If the radius r is, for example, 2 cm, then the radius of the large onion 2r is 4 cm.
The volume of a large sphere is always 8 times greater than the volume of a sphere with a half radius r.
V
_{1} = 4 / 3 ˣ π ˣ (2r)
^{3}
V
V_{2} = 4 / 3 ˣ π ˣ r
^{3}_{1} = 4 / 3 ˣ 3,14 ˣ (4 cm)
^{3}
V
V_{2} = 4 / 3 ˣ 3,14 ˣ (2 cm)
^{3}_{1} = 4,19 ˣ 64 cm
^{3}
V
_{2} = 4,19 ˣ 8 cm
^{3}V Volume of sphere / large onion_{1}:V Volume of sphere / small onion_{2}:r - Radius of a large onion_{1}: 2rr - Radius of a small onion_{2}: rπ: 3,14 - Ludolf's number
V
_{1} = 4 / 3 ˣ 3,14 ˣ 2r ˣ 2r ˣ 2rV _{2} = 4 / 3 ˣ 3,14 ˣ r ˣ r ˣ rV _{1} = 4,19 ˣ 8r^{3}V _{2} = 4,19 ˣ r^{3}V _{1} = 8 ˣ V_{2} |