Question

A solid cone of height 12cm and radius 9cm is recast into a solid sphere. Calculate the surface area of the sphere

Answer 1

volume of cone = (1/3)π(9^2)(12) = 324π cm^3

this becomes the volume of the sphere, so
(4/3)πr^3 = 324π
r^3 = 243
r = 6.24...

SA of sphere = 4πr^2 = 4π(6.24...)^2 = 489.34 cm^2

Answer 2

cone: v = 1/3 πr^2 h = 1/3 π * 9^2 * 12 = 324π
sphere: v = 4/3 πr^3 = 324π
so r^3 = 243
now, the area is 4πr^2 = ___

Answer 3

The result is written in a simplified form.

r³ = 243

r = ∛243

Since:

243 = 3⁵

r = ∛3⁵

r = ∛( 3³ ∙ 3² ) = ∛3³ ∙ ∛( 3² )

r = 3 ∛9 cm

Surface area of a sphere:

A = 4 π r²

A = 4 π ∙ ( 3 ∛9 )² = 4 π ∙ 3² ∙ ( ∛9 )² = 4 π ∙ 9 ∙ ∛9² = 36 π ∙ ∛81 =

36 π ∙ ∛( 27 ∙ 3 ) = 36 π ∙ ∛27 ∙ ∛3 = 36 π ∙ 3 ∙ ∛3

A = 108 π ∛3 cm²

Answer 4

Thanks so much

Answer 5

4πr^2
4×22/7×9×9
=1,018.3

Answer 6

489.4

Answer 7

I apologize for the mistake. The correct surface area of the sphere is 489.4 cm^2.