balloon has a circumference of 23 cm. Use the circumference to approximate the surface area of the balloon to the nearest square centimeter.

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

Surface Area = 4πr^2

First, we need to find the radius of the balloon. The circumference of a circle is related to its radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, the circumference is given as 23 cm:

23 cm = 2πr

To find the radius, we can rearrange the equation:

r = 23 cm / (2π)

Simplifying:

r ≈ 23 cm / (6.28)

r ≈ 3.66 cm (to two decimal places)

Now we can use this radius to approximate the surface area of the balloon:

Surface Area = 4π(3.66 cm)^2

Calculating:

Surface Area ≈ 4π(13.4256 cm^2)

Surface Area ≈ 53.7024 cm^2 (to four decimal places)

Therefore, the approximate surface area of the balloon to the nearest square centimeter is 54 cm^2.

To approximate the surface area of the balloon, you can use the formula for the surface area of a sphere, which is given by:

Surface Area = 4πr^2

However, in this case, we are given the circumference, not the radius. So, we need to find the radius first.

The formula for the circumference of a sphere is given by:

Circumference = 2πr

Since we are given the circumference as 23 cm, we can rearrange the formula to solve for the radius:

23 cm = 2πr

Now, divide both sides of the equation by 2π:

r = 23 cm / (2π)

Now, you can substitute this value of r back into the formula for the surface area:

Surface Area = 4π(23 cm / (2π))^2

Simplifying the equation, we get:

Surface Area ≈ 4π(23 cm)^2 / (4π^2)

Now, cancel out the π and square the radius:

Surface Area ≈ (23 cm)^2 / π

Finally, calculate the approximate surface area using a calculator and round the result to the nearest square centimeter.

Do you know what the formula for surface area is?

You may not have seen it like this, but

A = C/π