Answer:
113.04 in^3
Step-by-step explanation:
The surface area of a sphere of radius r is S = 4π*r^2. Here, S = 113.04 in^2. Equating this to the formula, we get 4π*r^2 = 113.04. We need to solve for the radius, r. Dividing both sides of this equation by 4π, we get:
r^2 = 113.04 / [4*3.14] = 9 in^2. Thus, the radius is r = 3 in.
The volume of this water balloon is given by V = (4/3)π*(3 in)^3, or
113.04 in^3.
The total amount of water will the balloon hold is 113.04 cubic inches and this can be determined by using the formula of volume and surface area of a sphere.
Given :
A spherical-shaped water balloon has a surface area of 113.04 square inches.
The following steps can be used in order to determine the amount of water will the balloon hold:
Step 1 - The surface area of the sphere is given below:
[tex]\rm A = 4\pi r^2[/tex]
Step 2 - Substitute the value of the surface area in the above expression.
[tex]\rm 113.04 = 4\pi r^2[/tex]
Simplify the above expression.
r = 3
Step 3 - Now, the volume of a sphere is given below:
[tex]\rm V = \dfrac{4}{3}\pi r^3[/tex]
Step 4 - Substitute the value of r in the above expression.
[tex]\rm V = \dfrac{4}{3}\times 3.14 \times 3^3[/tex]
Step 5 - Simplify the above expression.
V = 113.04 cubic inches
The total amount of water will the balloon hold is 113.04 cubic inches.
For more information, refer to the link given below:
https://brainly.com/question/2835293
