Question

A water balloon holds 904.78in ^3 of water. What is the diameter, in inches, of the balloon? Round to the nearest hundredth.

Answer 1

Diameter = 12.00 in

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:

`V=(4)/(3)\pi r^3`

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,

`904.78=(4)/(3)* (22)/(7)* r^3\\\\904.78=(88r^3)/(21)\\\\88r^3=904.78* 21\\\\r^3=(19000.38)/(88)\\\\r^3=215.9134\\\\r=\sqrt[3]{215.9134}=5.9992\ in`

Now, diameter is equal to twice of radius. Therefore,

`d=2r=2* 5.9992=11.998\approx12.00\ in(Nearest\ hundredth)`

Therefore, the diameter of the balloon is 12.00 inches.