Answer: The total volume of concrete that Jimmy will need to create the 4 spheres is 38.25 cubic feet, rounded to the nearest whole number.
Explanation:
To find the total volume of concrete needed for the 4 spheres, we need to find the volume of each sphere individually and then add them up. The formula for the volume of a sphere is (4/3)πr^3, where r is the radius of the sphere.
First, we need to find the radius of the largest sphere, which is 4 feet in diameter. The radius is half the diameter, so it is 2 feet.
The radius of the next sphere is half of the radius of the first sphere, which is 1 foot.
The radius of the next sphere is half of the radius of the second sphere, which is 0.5 feet.
The radius of the last sphere is half of the radius of the third sphere, which is 0.25 feet.
We can now use the formula to find the volume of each sphere and then add them up.
The volume of the first sphere = (4/3)π(2^3) = (4/3)π(8) = 33.49 cubic feet
The volume of the second sphere = (4/3)π(1^3) = (4/3)π(1) = 4.19 cubic feet
The volume of the third sphere = (4/3)π(0.5^3) = (4/3)π(0.125) = 0.52 cubic feet
The volume of the last sphere = (4/3)π(0.25^3) = (4/3)π(0.015625) = 0.05 cubic feet
Total volume of all spheres = 33.49 + 4.19 + 0.52 + 0.05 = 38.25 cubic feet
The total volume of concrete that Jimmy will need to create the 4 spheres is 38.25 cubic feet, rounded to the nearest whole number.