Answer:
Diameter = 12.00 in
Step-by-step explanation:
Given:
Capacity of water balloon (V) = 904.78 in³
Let the diameter of the water balloon be 'd' inches.
Assuming the water balloon is spherical in shape.
We know that, volume of a sphere is given as:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Where 'r' is the radius of the sphere.
Use π = 22/7
Now, plug in the given values and solve for radius 'r'. This gives,
[tex]904.78=\frac{4}{3}\times \frac{22}{7}\times r^3\\\\904.78=\frac{88r^3}{21}\\\\88r^3=904.78\times 21\\\\r^3=\frac{19000.38}{88}\\\\r^3=215.9134\\\\r=\sqrt[3]{215.9134}=5.9992\ in[/tex]
Now, diameter is equal to twice of radius. Therefore,
[tex]d=2r=2\times 5.9992=11.998\approx12.00\ in(Nearest\ hundredth)[/tex]
Therefore, the diameter of the balloon is 12.00 inches.
