Respuesta :
Answer:
When the sphere has a radius of length 3, the value of the volume of a sphere becomes equal to the value of the surface area of the same sphere.
Step-by-step explanation:
Given R is the radius of a sphere.
Volume of a sphere is given by the formula
\frac{4}{3} × π × R³.
While, surface area of a sphere is given by the formula
4 × π × R².
We need to find the value of radius, R, for which the value of the volume of a sphere equals the value of the surface are of a sphere.
As per the question, we begin with the assumption that the value of the volume of a sphere equals the value of the surface area of the sphere.
This is shown in the form of an equation given below.
\frac{4}{3} × π × R³ = 4 × π × R²
On both sides of the equation, π, is a common term. Hence, this term can be removed from both the sides.
⇒ \frac{4}{3} × R³ = 4 × R²
Similarly, R², is common on both sides of the equation. Next, this term is removed from both the sides of the above equation.
⇒ \frac{4}{3} × R = 4
Next, 4 is the numerator on both sides of the equation.
4 is removed in the next step from both sides.
We get the equation as shown below.
⇒ \frac{1}{3} × R = 1
In the above equation, only term left is R, the radius of the sphere.
On further solving the equation, we get the value of R as 3, which is shown below.
⇒ \frac{R}{3} = 1
On transferring 3 to the other side, we get the value of R as 3.
⇒ R = 1 x 3
⇒ R = 3
Hence, for the radius of 3, both the volume of the sphere and the surface area of the sphere become equal.
