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snow_tiger [21]
3 years ago
7

a solid sphere is cut into 3 equal wedges. the volume of each wedge is V=4/9π^3. solve the formula for r

Mathematics
2 answers:
forsale [732]3 years ago
7 0

Step-by-step explanation:

hmmm.

the other answer says the volume of a wedge is

4/9 × pi×r³

but I read here only

4/9 × pi³

so, what is correct ?

if I assume my reading is correct, then the solution is actually

4/9 × pi×r³ = 4/9 × pi³

pi×r³ = pi³

r³ = pi²

r =  \sqrt[3]{ {\pi}^{2} }

and that would mean

r ≈ 2.145

algol133 years ago
4 0

\\ \qquad\quad\sf{:}\dashrightarrow V=\dfrac{4}{9}πr^3

  • It is one third of the solid. sphere

\\ \qquad\quad\sf{:}\dashrightarrow V_{(Sphere)}

\\ \qquad\quad\sf{:}\dashrightarrow 3\left(\dfrac{4}{9}πr^3\right)

\\ \qquad\quad\sf{:}\dashrightarrow \dfrac{4}{3}\pi r^3

Now

\\ \qquad\quad\sf{:}\dashrightarrow \pi r^3=\dfrac{3V}{4}

\\ \qquad\quad\sf{:}\dashrightarrow r^3=\dfrac{3V}{4\pi}

\\ \qquad\quad\sf{:}\dashrightarrow r=\sqrt[3]{\dfrac{3V}{4\pi}}

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