The volume of a sphere is 11,488.21ft cubed. To the nearest foot, what is the radius of the sphere? Use 3.14 for pie.
The formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume, π is the constant 3.14, and r is the radius.
To solve for r, we can rearrange the formula to:
r = (3V/4π)^(1/3)
Plugging in the given volume, we get:
r = (3(11488.21)/(4*3.14))^(1/3) ≈ 16.0
So the radius of the sphere is approximately 16 feet.
The volume of a sphere is 5,572.45m cubed . To the nearest meter, what is the radius of the sphere? Use 3.14 for pie.
The formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume, π is the constant 3.14, and r is the radius.
To solve for r, we can rearrange the formula to:
r = (3V/4π)^(1/3)
Plugging in the given volume, we get:
r = (3(5572.45)/(4*3.14))^(1/3) ≈ 11.0
So the radius of the sphere is approximately 11 meters.
A spherical balloon has a 16-in. diameter when it is fully inflated. Half of the air is let out of the balloon. Assume that the balloon remains a sphere. Find the volume of the fully-inflated balloon
The diameter of the fully inflated balloon is 16 inches, which means the radius is 8 inches (half the diameter).
The formula for the volume of a sphere is:
V = (4/3)πr³
where π is approximately 3.14 and r is the radius.
Plugging in the radius of 8 inches, we get:
V = (4/3)π(8³)
V = (4/3)(3.14)(512)
V = 2143.57 cubic inches (rounded to two decimal places)
Therefore, the volume of the fully inflated balloon is approximately 2143.57 cubic inches.
To find the radius of a sphere given its volume, you can use the formula for the volume of a sphere:
V = (4/3) * π * r³,
where V is the volume, π is a mathematical constant approximately equal to 3.14, and r is the radius.
In this case, the volume of the sphere is given as 11,488.21 ft³. We can plug this value into the formula and solve for r:
11,488.21 = (4/3) * 3.14 * r³.
To isolate r, we can rearrange the equation:
r³ = (11,488.21) / ((4/3) * 3.14).
Simplifying the right side:
r³ = 2,895.97 / 4.19.
r³ ≈ 690.68.
To find the approximate value of r, we can calculate the cube root of 690.68:
r ≈ ∛(690.68).
Using a calculator, the cube root of 690.68 is approximately 8.805.
Therefore, the radius of the sphere to the nearest foot is 9 feet (rounded up from 8.805 feet).