One large bubble separates into four small bubbles so that the total area of the small bubbles is equal to the area of the large bubble. Each small bubble has a radius of 5 centimeters. What is the radius of the large bubble?

10 cm.

Step-by-step explanation:

We'll begin by calculating the area of the small bubble. This can be obtained as follow:

Radius (r) = 5 cm

Area (A) =?

Since the bubble is circular in nature, we shall use the formula for area of circle to determine the area of the bubble. This is illustrated below:

A = πr²

A = π × 5²

A = 25π cm²

Next, we shall determine the total area of the small bubbles. This can be obtained as follow:

Area of 1 bubble = 25π cm²

Therefore,

Area of 4 bubbles = 4 × 25π cm²

Area of 4 bubbles = 100π cm²

Finally, we shall determine the radius of the large bubble. This can be obtained as follow:

Area of large bubble = total area of small bubbles = 100π cm²

Radius (r) =?

A = πr²

100π = πr²

100 = r²

Take the square root of both side

r = √100

r = 10 cm

Thus, the radius of the large bubble is 10 cm