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

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:

$V=\frac{4}{3}\pi r^3$

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,

$904.78=\frac{4}{3}\times \frac{22}{7}\times r^3\\\\904.78=\frac{88r^3}{21}\\\\88r^3=904.78\times 21\\\\r^3=\frac{19000.38}{88}\\\\r^3=215.9134\\\\r=\sqrt[3]{215.9134}=5.9992\ in$

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

$d=2r=2\times 5.9992=11.998\approx12.00\ in(Nearest\ hundredth)$

Therefore, the diameter of the balloon is 12.00 inches.