4. 8.G.3.9
This cone and sphere have equal volumes.

What is the radius of the sphere?

the radius of the sphere is 12 cm.

Step-by-step explanation:

IN A CONE

vertical height (h) = 27 cm

radius (r) = 32 / 2 = 16 cm

Now the volume of cone is

= 1/3 *h*π*r²

= 1/3 * 27 *π *16²

= 2304π cm³

Also by the question the cone and the sphere have equal volumes so

volume of sphere = volume of cone

                             = 2304 π cm³

OR, 4/3 πr³ = 2304 π

4/3 * r³ = 2304

r³ = 2304 * 3 / 4

r³ = 1728

r = ∛1728

r = 12 cm

hope it helps :)

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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