Damari inflates a spherical balloon to twice its original radius. Explain to Damari why the surface area is 4 times as big when the radius is doubled.

The easiest way is to show him the formula for the area of a sphere:
Area = 4 π (radius)²
That's a good thing to discuss, because it's a good thing to remember, and discussing it will help him remember it.
The important part to look at is the part where it says "** (radius)² **" . That tells you that if you multiply the radius by (Anything), then the area is multiplied by (Anything)² .
Since he multiplied the radius by 2, the area was multiplied by (2)² = 4 .

Answered by AL2006 | 2024-06-10

Surface area is directly proportional to the square of radius.
Thus, when radius is doubled, Surface area becomes 2² = 4 times.

Answered by tadvisohil886 | 2024-06-10

When the radius of a spherical balloon is doubled, the surface area increases by a factor of 4 due to the formula for surface area being proportional to the square of the radius. Specifically, if the original radius is r , the new surface area becomes 16 π r 2 , which is 4 times the original area of 4 π r 2 . Thus, doubling the radius leads to a quadrupling of the surface area.
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Answered by AL2006 | 2024-12-23