Question

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

Answer 1

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

Answer 2

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

• 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

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

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

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