Question

The volume of a sphere is 5,000pi m3. What is the surface area of the sphere to the nearest square meter?

Answer 1

The surface area of the sphere with a volume of 5,000pi m3 is calculated to be approximately 3,065 square meters when using the sphere volume and surface area formulae.

Step-by-step explanation:

To find the surface area of a sphere when given its volume, we can use the volume and surface area formulae for a sphere. The formula for the volume of a sphere is V = 4/3 (pi) (r)^3, and for surface area it is A = 4 (pi) (r)^2.

Given that the volume V of the sphere is 5,000pi m3, we can solve for the radius (r) and then use that to calculate the surface area (A). Working through the volume formula:

V = 4/3 (pi) (r)^3 = 5,000pi
So, (r)^3 = (3/4) * 5,000
r^3 = 3,750
r = ∛(3,750)
r ≈ 15.59 meters

Substituting r into the surface area formula:

A = 4 (pi) (r)^2
A = 4 * pi * (15.59)^2 ≈ 3,065 to the nearest square meter.

Answer 2

To get the surface area of the sphere, we need to know the radius. Since the volume is given, we can get the radius.
Volume =
`(4)/(3)`π r³
5000πm³ =
`(4)/(3)` π r³
5000m³ =
`(4)/(3)` r³
5000m³ x 3 = 4r³

`(15000m³)/(4)` =
`(4r³)/(4)`
∛3750 = ∛r³

r = 15.536m
r = 15.54m
Since the radius is now known, substitute it directly to the surface area formula
A = 4π x r²
A = 4π x (15.54)²
A= 3,034.67 m² or 3,035 m²