Volume of a sphere:
\(V = \frac{4}{3}\pi r^3\)
Combining dough is like combining volume. So we get
\(V_3=\frac{4}{3}\pi r_3^3=\frac{4}{3}\pi r_1^3 + \frac{4}{3}\pi r_2^3 = \frac{4}{3}\pi (r_1^3+r_2^3)\)
Where \(V_3\) is the combined volume of dough of radii \(r_1\) and \(r_2\)
The new radius is therefore
\(r_3^3=r_1^3+r_2^3\)
Substituting values we get
\(r_3^3=3^3+5^3=27+125=152\)
\(r_3=\sqrt[3] 152 \approx 5.34\)
So the new dough is 5.34 cm, just a bit larger.
Cylinders:
\(V=\pi r^2 h\)
So volume is directly proportional to height, if radius is constant. So ratios stay the same. 75/25=3 and the volume is also 3 times larger (ratio 3:1).
