Respuesta :
The surface area of the sphere is given by the equation
[tex]A=4\pi * r^{2}[/tex],
where A is the surface area and r is the radius.
We want to find the volume of the sphere, which is given by the equation
[tex]V = \frac{4}{3} * \pi * r^{3}[/tex],
where V is the volume and r is the radius.
Looking at these equations, we see that they both involve the sphere's radius. If we know what r is, we can calculate the volume.
We know that the sphere's surface area is [tex]36 \pi[/tex]. Plugging that in for A in the surface area equation, we get
[tex]36 \pi=4\pi * r^{2}[/tex], then divide by [tex]\pi[/tex]
[tex]36 = 4 * r^{2}[/tex], then divide by 4
[tex]r^{2} = 9[/tex], then take the square root of both sides
[tex]r = 3[/tex]
So the radius of the sphere is 3. Plugging this into the volume equation,
[tex]V = \frac{4}{3} * \pi * 3^{3}[/tex], simplify terms
[tex]V = \frac{4}{3} * \pi * 27[/tex], multiply [tex]\frac{4}{3}[/tex] by 27
[tex]V = 36 * \pi[/tex]
So the volume of the sphere is [tex]36\pi[/tex].
Answer:
36π ft^3
Step-by-step explanation:
The surface area (S) of a sphere can be defined as:
S = 4×π×r^2 = 36×π
Solve for r to get the radius of the sphere:
r = ([tex]\sqrt{36/4}[/tex] = 3
The voluem (V) of a sphere can be defined as:
V= (4/3)×π×r^3
The volume of the sphere is:
V = (4/3)×π×(3^3) = 36π ft^3
The volume of the sphere can be calculated from the surface area given.
