A manufacturer drills a hole through the center of a metal sphere of radius R = 8. The hole has a radius r. What value of r will produce a ring whose volume is exactly half the volume of the sphere? (Round your answer to two decimal places.)

New radius(r) = 3.65 (Approx)

Step-by-step explanation:

Given:

Radius of sphere(R) = 8

Find:

New radius(r)

Computation:

Volume of sphere = (4/3)πR³

Volume of sphere = (4/3)π(6)³

Volume of sphere = 288π

Volume of ring = (4/3)π(R²-r²)³/²

Half volume of sphere = Volume of ring

288π / 2 = (4/3)π(R²-r²)³/²

144 = (4/3)(6²-r²)³/²

108 = (6²-r²)³/²

New radius(r) = 3.65 (Approx)

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step-by-step explanation:

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step-by-step explanation:

. your answer will contain x - and y -terms. (1 point) x ( ¿¿ 2 − 7 ) 2 +( y 2 − 9 ) 2 √ ¿ 12. what is the distance from the directrix (the crocodile river) to the point ( x , y )? write this equation. your answer will contain a y -term.