Respuesta :
The diameter of a sphere is 20.32 m
Explanation:
Given:
Volume of the sphere, V = 4397m³
Diameter, D = ?
We know,
Volume of the sphere = [tex]\frac{4}{3} \pi r^3[/tex]
Where,
r = radius of the sphere
On substituting the value in the formula we get:
[tex]4397 = \frac{4}{3} \pi (r)^3\\\\r^3 = \frac{4397 X 3}{4\pi } \\\\r^3 = 1049.7 m^3\\\\r = 10.16m[/tex]
Diameter = 2 X radius
D = 2 X 10.16 m
D = 20.32 m
Therefore, the diameter of a sphere is 20.32 m
the diameter of a sphere is [tex]20.3m[/tex] .
Step-by-step explanation:
Here we have , a sphere with a volume of 4397 m^3 . We need to find the diameter of sphere . Let's find out:
We know that , Volume of sphere is given by formula as :
⇒ [tex]Volume =\frac{4}{3}\pi r^3[/tex] .......(1)
According to question we have following parameters as :
[tex]Volume = 4397m^3\\Radius = \frac{Diameter}{2}[/tex]
Putting these values in we get:
⇒ [tex]Volume =\frac{4}{3}\pi r^3[/tex]
⇒ [tex]4397 =\frac{4}{3}\pi (\frac{D}{2}) ^3[/tex]
⇒ [tex]4397 =\frac{4}{3}\pi (\frac{D^3}{8})[/tex]
⇒ [tex]4397 =\pi (\frac{D^3}{6})[/tex]
⇒ [tex]D^3 =6 (\frac{4397}{\pi})[/tex]
⇒ [tex]D^3 =6 (\frac{4397}{3.14})[/tex]
⇒ [tex]D^3 =8402[/tex]
⇒ [tex]D =\sqrt[3]{ 8402}[/tex]
⇒ [tex]D =20.3m[/tex]
Therefore , the diameter of a sphere is [tex]20.3m[/tex] .
