A balloon has a circumference of 11 cm. Use the circumference to approximate the surface area of the balloon to the nearest square centimeter.
SA = 4πr^2
C = 2πr
we know 2πr = 11
2r = 11/π
so the surface area is
4πr^2 = (2πr)(2r) = 11(11/π) = 121/π = 39 cm^2
The word "approximate" here puzzles me.
It suggests that we do 121/π in our head, not too many students could do that.
Unless this is an old-fashioned textbook question and they want us to use 22/7 for π
then 121/(22/7)
= 121*7/22
= 11*7/2
= 77/2 = 38.5 or 39 as above
circumference (c) is ... 2 * π * r
... r = c / (2 π)
surface area (s) is ... 4 * π * r^2 = 4 * π * c^2 / (4 π^2) = c^2 / π
To approximate the surface area of the balloon, we will assume that it is a perfect sphere. The formula for the surface area of a sphere is:
Surface Area = 4 * π * r^2
Given that the circumference of the balloon is 11 cm, we can solve for the radius (r):
Circumference = 2 * π * r
11 = 2 * π * r
To find r, divide both sides of the equation by 2 * π:
r = 11 / (2 * π)
Now we can calculate the surface area of the balloon using the formula:
Surface Area ≈ 4 * π * (11 / (2 * π))^2
Simplifying further:
Surface Area ≈ 4 * π * (121 / (4 * π^2))
Surface Area ≈ 121 cm^2 (rounded to the nearest whole number)
Therefore, the surface area of the balloon, approximated to the nearest square centimeter, is 121 cm^2.
To approximate the surface area of a balloon using its circumference, we need to make a couple of assumptions. First, we'll assume that the balloon is a perfect sphere, which is a common shape for balloons. Second, we'll assume that the circumference of a sphere is proportional to its surface area.
The formula for the circumference of a sphere is given by:
C = 2πr
Where:
C is the circumference
π (pi) is a mathematical constant approximately equal to 3.14159
r is the radius of the sphere
In this case, we are given the circumference (C) as 11 cm. We can rearrange the formula to solve for the radius (r):
C = 2πr
11 = 2πr
To find the surface area, the formula for the surface area of a sphere is given by:
A = 4πr^2
Substituting the value of the radius, we can calculate the surface area.
First, let's solve for the radius (r):
11 = 2πr
Divide both sides by 2π:
r = 11 / (2π)
Now, we can calculate the surface area (A):
A = 4πr^2
A = 4π(11 / (2π))^2
Simplifying the equation:
A = 4π(121 / (4π^2))
A = 121 / π
Since we need to approximate the answer to the nearest square centimeter, we need to evaluate the value of π. Using 3.14159 as an approximation for π, we can calculate the surface area:
A ≈ 121 / 3.14159
A ≈ 38.42
Rounding the surface area to the nearest square centimeter, we get:
A ≈ 38 cm^2
Therefore, the approximate surface area of the balloon is 38 square centimeters.