Question

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?

Answer 1

Answer:

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