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  • 13-05-2021
  • Mathematics
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4. 8.G.3.9
This cone and sphere have equal volumes.

What is the radius of the sphere?

4 8G39 This cone and sphere have equal volumes What is the radius of the sphere class=

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kritika3375
kritika3375 kritika3375
  • 13-05-2021

Answer:

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 :)

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