Question

Cylinders A and B are congruent. Cylinder A has a volume of 27π cm3 and a height of 3 cm. What is the diameter of Cylinder B?

Answer 1

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

$diameter = 2*r_{B}= 2* 3cm=6cm$

Answer 2

V = πR²h = π*R²*3
27π = 3πR²
R² = 9
R = 3

Diameter = 3*2 = 6cm