A spherical balloon has a circumference of 25 cm.
a.) What is the approximate surface area of the balloon to the nearest square centimeter?
b.) What is the approximate volume of the balloon to the nearest cubic centimeter?
recall that
A = 4πr^2
V = 4/3 πr^3
and since C = 25, r = 25/(2π)
To find the surface area of the balloon, we can use the formula for the surface area of a sphere: A = 4πr², where A is the surface area and r is the radius of the sphere.
a) To find the radius of the balloon, we can use the formula for the circumference of a sphere: C = 2πr, where C is the circumference and r is the radius of the sphere.
In this case, the given circumference of the balloon is 25 cm. So we can solve for r as follows:
25 cm = 2πr
Divide both sides of the equation by 2π:
r = 25 cm / (2π) ≈ 3.98 cm (rounded to two decimal places)
Now that we have the radius, we can find the surface area of the balloon:
A = 4π(3.98 cm)² ≈ 200.64 cm² (rounded to the nearest square centimeter)
Therefore, the approximate surface area of the balloon is approximately 200.64 square centimeters.
b) To find the volume of the balloon, we can use the formula for the volume of a sphere: V = (4/3)πr³, where V is the volume and r is the radius of the sphere.
Using the radius calculated earlier (approximately 3.98 cm), we can find the volume of the balloon:
V = (4/3)π(3.98 cm)³ ≈ 267.79 cm³ (rounded to the nearest cubic centimeter)
Therefore, the approximate volume of the balloon is approximately 267.79 cubic centimeters.