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

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=(4)/(9)πr^3`

• It is one third of the solid. sphere

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

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

`\\ \qquad\quad\sf{:}\dashrightarrow (4)/(3)\pi r^3`

Now

`\\ \qquad\quad\sf{:}\dashrightarrow \pi r^3=(3V)/(4)`

`\\ \qquad\quad\sf{:}\dashrightarrow r^3=(3V)/(4\pi)`

`\\ \qquad\quad\sf{:}\dashrightarrow r=\sqrt[3]{(3V)/(4\pi)}`