A solid cone of height 12cm and radius 9cm is recast into a solid sphere. Calculate the surface area of the sphere
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
Thanks so much
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 = ___
4πr^2
4×22/7×9×9
=1,018.3
489.4
I apologize for the mistake. The correct surface area of the sphere is 489.4 cm^2.
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