Answered

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A sphere has a radius of 2 inches. What is the approximate volume of half of the sphere?

Sagot :

  • radius=r=2in

Volume:-

[tex]\\ \rm\Rrightarrow V=\dfrac{4}{3}\pi r^3[/tex]

[tex]\\ \rm\Rrightarrow V=\dfrac{4}{3}\pi (2)^3[/tex]

[tex]\\ \rm\Rrightarrow V=\dfrac{32\pi}{3}in^3[/tex]

Half volume:-

[tex]\\ \rm\Rrightarrow V=\dfrac{16\pi}{3}in^3[/tex]

semsee45

Answer:

16.8 in³ (nearest tenth)

Step-by-step explanation:

Volume of a sphere

[tex]V=\dfrac43 \pi r^3[/tex]

(where V is volume and r is the radius)

Volume of a hemisphere

[tex]\textsf{Volume of a hemisphere}=\dfrac12 \ \textsf{Volume of a Sphere}[/tex]

[tex]\implies V=\dfrac12 \cdot \dfrac43 \pi r^3=\dfrac23 \pi r^3[/tex]

Given:

  • r = 2 in

[tex]\begin{aligned}\implies V & =\dfrac23 \pi (2)^3\\\\ & =\dfrac{16}{3} \pi\\\\ & =16.8 \ \sf in^3 \ (nearest \ tenth)\end{aligned}[/tex]

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