A balloon has a circumference of 16 cm. Use the circumference to approximate the surface area of the balloon to the nearest square centimeter.

Question

(1 point)
Responses

804 cm2
804 cm 2

326 cm2
326 cm 2

256 cm2
256 cm 2

81 cm2

Answer 1

To approximate the surface area of the balloon, we can use the formula for the surface area of a sphere:

Surface Area = 4πr^2

Since the balloon's circumference is given, we can use the formula for the circumference of a circle to find the radius:

Circumference = 2πr

Solving for the radius (r), we divide the circumference by 2π:

16 cm = 2πr

Dividing both sides by 2π, we get:

r = 16 cm / (2π) ≈ 2.546 cm

Now, we can substitute the value of the radius into the formula for surface area:

Surface Area = 4π(2.546 cm)^2 ≈ 81 cm^2

Therefore, the approximate surface area of the balloon is 81 cm^2.