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marshall27 [118]
3 years ago
7

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?

Mathematics
2 answers:
Llana [10]3 years ago
8 0

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

Ann [662]3 years ago
6 0
V = πR²h = π*R²*3
27π = 3πR²
R² = 9
R = 3

Diameter = 3*2 = 6cm
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