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The volume of a sphere is 2254 pi m^3 what is the surface area of the sphere to the nearest 10th
a.831.4 m^2
b.891.6 m^2
c.1220.0 m^2
d.1783.3 m^2

Respuesta :

carlosego
By definition. The volume of the sphere is:
 V = (4/3) * (pi) * (r ^ 3)
 Where,
 r: radius of the sphere.
 Substituting values:
 2254 pi = (4/3) * (pi) * (r ^ 3)
 Clearing the radio we have:
 r ^ 3 = (3/4) * (2254)
 r = ((3/4) * (2254)) ^ (1/3)
 r = 11.91255883
 Then, the surface area is:
 A = 2 * pi * r ^ 2
 Substituting values:
 A = 2 * 3.14 * (11.91255883) ^ 2
 A = 891.6 m ^ 2
 Answer:
 The surface area of the sphere is:
 b. 891.6 m ^ 2

The surface area of a sphere with volume of 2254π m³ is 1782 m²

How to find volume of a sphere?

volume of a sphere = 4 / 3 πr³

where

  • r = radius

Therefore,

2254π = 4 / 3 πr³

2254π × 3 = 4πr³

6762π = 4πr³

r³ = 6762π / 4π

r = ∛1690.5

r = 11.9125588

r = 11.91 m

Therefore,

surface area of sphere = 4πr²

surface area of sphere = 4 × 3.14 × 11.91²

surface area of sphere = 1781.612136

surface area of sphere = 1782 m²

learn more on sphere here: https://brainly.com/question/12768794

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