A spherical balloon has a radius of 9 centimeters. Find the amount of air required to fill the balloon. Round to the nearest hundredth
recall the formula for the volume of a sphere
v = 4/3 pi r^3
v(9) = 4/3 pi * 729
= 972 pi
= 3053.63 cm^3
To find the amount of air required to fill the balloon, we need to calculate the volume of the balloon. The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.
Given that the radius of the balloon is 9 centimeters, we can substitute this value into the formula:
V = (4/3)π(9^3)
First, we need to calculate 9^3:
9 × 9 × 9 = 729
Substituting this value into the formula:
V = (4/3)π(729)
Next, we multiply 729 by (4/3):
(4/3) × 729 = 972
Finally, we multiply 972 by π (pi) to get the approximate volume of the balloon:
V ≈ 972π
To round to the nearest hundredth, we can use the approximate value of π as 3.14:
V ≈ 972 × 3.14
Now, we can calculate the volume of the balloon:
V ≈ 3050.08 cubic centimeters
Therefore, the amount of air required to fill the balloon is approximately 3050.08 cubic centimeters when rounded to the nearest hundredth.