Question

a solid sphere is cut into 3 equal wedges. the volume of each wedge is ( v = \frac{4}{9}pi r^3 ). solve the formula for ( r ).
a. ( r = sqrt3{9v - 4pi} )
b. ( r = sqrt3{\frac{4pi}{9v}} )
c. ( r = sqrt3{9v(4pi)} )
d. ( r = sqrt3{\frac{9v}{4pi}} )

Explanation:

Step1: Start with given formula

$V = \frac{4}{9}\pi r^3$

Step2: Isolate $\pi r^3$

Multiply both sides by 9: $9V = 4\pi r^3$

Step3: Isolate $r^3$

Divide by $4\pi$: $r^3 = \frac{9V}{4\pi}$

Step4: Solve for $r$

Take cube root: $r = \sqrt[3]{\frac{9V}{4\pi}}$

Answer:

D. $r = \sqrt[3]{\frac{9V}{4\pi}}$