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if a sphere has the same volume as a cube with edge length 5, estimate the radius of the sphere

Sagot :

absor201

Answer:

The radius of the sphere will be:

  • [tex]r=3.1[/tex] units

Step-by-step explanation:

Given that a sphere has the same volume as a cube with edge length 5.

[tex]V_c=V_s[/tex]

[tex]\:a^3=\frac{4}{3}\pi r^3[/tex]

[tex]\:r^3=\frac{3\:a^3}{4\pi }[/tex]

[tex]\:\:r=\sqrt[3]{\frac{3\:a^3}{4\pi \:}\:\:}[/tex]

substitute a = 5

[tex]r=\sqrt[3]{\frac{3\:\left(5\right)^3}{4\pi \:\:\:}\:\:}[/tex]

[tex]r=3.1[/tex] units

Therefore, the radius of the sphere will be:

  • [tex]r=3.1[/tex] units
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