Answer:
diameter = 6 cm
Step-by-step explanation:
Two cylinders are congruent when they have the same size and dimensions. In that respect, it is possible to use mathematical criteria for determining the previous statement as follows;
If the cylinder A and B are congruent, then the volume is equivalent to
\(V_A=V_B\)
Reminding the volume of the cylinder can be determined by
\(V=\pi r^2h\), where r is the radius of the cylinder and h the height. With the given data from the problem, it substitutes the values as follows,
\(27cm^3=(3cm)* \pi r_{B}^2\)
To determine the diameter of the cylinder B is necessary to calculate its radius, thus;
\(r_{B}^2=\frac{27cm^3}{(3cm)* \pi} \\ \sqrt{r_{B}^2} =\sqrt{\frac{27cm^3}{(3cm)* \pi}} \\r_{B}=3 cm\)
Reminding the radius of the cylinder corresponds to the radius of any circle of which the diameter is the double of its radius, then
\(diameter = 2*r_{B}= 2* 3cm=6cm\)
