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The diameter of a sphere is 8 centimeters. What is the volume of the sphere? Use 3.14 for pi. Enter your answer, as a decimal, in the box. Round only your final answer to the nearest tenth. cm³

Respuesta :

susanwiederspan
The volume of a sphere is given by the equation [tex]V= \frac{4}{3} \pi r^3[/tex], where r is the radius.

We are given the diameter of the sphere, but recall that the diameter is twice the radius: [tex]d=2r[/tex]. So the radius is half of the diameter: [tex]r= \frac{1}{2}d[/tex].

Half of 8 cm is 4 cm.

We substitute this for r in the equation and we use 3.14 for π.

[tex]V= \frac{4}{3}(3.14)(4)^3= \frac{(4^4)(3.14)}{3}=267.9 \ cm^3 [/tex]
jimman
the steps for this are below

recall volume of sphere formula is
[tex] \frac{4}{3} \pi \times r {}^{3} [/tex]
we know the diameter so to get the radius we just divide the diameter by 2 to get the radius
[tex]r = 8 \div 2[/tex]
[tex]r = 4[/tex]
know we can plug it into the volume of a sphere formula and solve using 3.14 for pi
[tex]v = (4 \times 3.14 \times 4 {}^{3} ) \div 3[/tex]
simplify the parentheses and get
[tex]v = \frac{803.84}{3} [/tex]
FINAL ANSWER (rounding to nearest tenth)
[tex]v = 267.9 \: cm {}^{3} [/tex]


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