How much larger is the calculation of the volume of a sphere whose radius is 69 inches if π is used instead of 3.14? Round your answer to the nearest tenth.
To find the volume of a sphere, we use the formula V = (4/3)πr^3, where r is the radius of the sphere.
Using the given radius of 69 inches and π as 3.14:
V = (4/3)(3.14)(69)^3
V ≈ (4/3)(3.14)(328,509)
V ≈ 1,387,750.8 cubic inches
Now, let's find the volume using the accurate value of π:
V = (4/3)(π)(69)^3
V ≈ (4/3)(3.14159265359)(328,509)
V ≈ 1,387,780.2 cubic inches
To find how much larger this calculation is, we subtract the first volume from the second volume:
1,387,780.2 - 1,387,750.8 ≈ 29.4 cubic inches
Therefore, the calculation of the volume of a sphere is about 29.4 cubic inches larger when the accurate value of π is used instead of 3.14.