Respuesta :
Answer:
Step-by-step explanation:
the volume of a sphere is
V= (4/3)*3.14*r^3
89,110=4/3 * 3.14* r^3
89110/3.14=4/3*r^3
28,378.98=4/3*r^3
(3*28,378.98)/4=r^3
21,284.23=r^3
r=[tex]\sqrt[3]{21284.23}[/tex]=27.71
d=2*r=55.42 cm rounded is 55 cm
The diameter of the sphere is 55.4 cm where its volume is given as 89110 cm³. This is obtained by equating the volume of the given sphere with the standard formula, we get the radius and we know that twice a radius is the diameter.
The volume of the sphere:
The standard formula for the volume of a sphere is given as
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
where r is the radius of the sphere
Diameter:
The diameter of a sphere is twice its radius i.e.,
d = 2r
Calculating the diameter for the given sphere:
It is given that volume of the sphere V = 89110 cm³
On substituting,
[tex]89110 = \frac{4}{3}\pi r^{3}[/tex]
⇒ [tex]r^{3}=\frac{267330}{4\pi}[/tex]
⇒ [tex]r^{3}=21273.44[/tex]
⇒ [tex]r=\sqrt[3]{21273.44}[/tex]
⇒ r = 27.708
Then,
Diameter d = 2 × r
= 2 × 27.708
= 55.41
Rounding the obtained value to the nearest tenth results in 55.4
Therefore, the diameter of the given sphere with a volume of 89110 cm³ is 55.4 cm
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