0
If you double the diameter of a circle, the area will quadruple (be 4x greater).
The area of the circle increases exponentially with the diameter, or more precisely with the radius, which is 1/2 the diameter. A = (pi)r2
Doubling the diameter of a circle will quadruple the area (22 =4).
This is easily seen in pizzas, where the dough needed for a 16-inch Pizza can be used instead to make 4 pizzas with a diameter of 8 inches.
---
The equation to find the area of a circle is a=(pi)r2. If the diameter is doubled, then the radius is also doubled, because the radius is just half the diameter.
The area of a circle once its radius (and therefore diameter) has been doubled can be expressed as follows: a'=(pi)(2r)2, which simplifies to a'=(pi)(4r2).
To find the proportion of a' and a, we just divide the second by the first. This gets us
[(pi)(4r2)]/[(pi)(r2)]=4
Still curious? Ask our experts.
Chat with our AI personalities
Professor
Jordan
BlakeAdd your answer:
Earn +20 pts
What happens to a circle when the radius is doubled?
The area quadruples.
What happens to the area of a circle when the radius is doubled tripled?
The area increases as the square of the radius (or diameter). So if you double the radius you * 4 (quadruple) the area. Treble the radius, you *9 the area.
What happens to the area of a circle when the circumference is doubled?
It becomes twice as large
What happens to the area of a circle if yo double the radius?
Nothing - if you double the radius you will get the diameter. The area of the circle will remain the same
What happens to the volume of a cylinder if the height is doubled and the diameter of the base is not changed?
since the volume of a right cylinder is height x area of base, the area of the baseis Pi * r^2 (r is radius which is 1/2 of diameter), so the area of the base did notchange, while the height is doubled so the volume is doubled.
