When the diameter of a circle is tripled, the area of the circle will be increased by how many times?
Created: 2 years ago |
Updated: 7 months ago
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When the diameter of a circle is tripled, the area of the circle is increased by 9 times.
The area of a circle is given by the formula A = πr², where "r" is the radius of the circle.
If the diameter is tripled, the new diameter is 3 times the original diameter. Since the radius is half of the diameter, the new radius will also be 3 times the original radius.
Let A₁ be the original area (πr²) and A₂ be the new area (π(3r)²).
A₂ = π(3r)² = π(9r²) = 9πr².
So, the new area A₂ is 9 times the original area A₁. Therefore, when the diameter is tripled, the area of the circle is increased by 9 times.
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