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A sphere is a three-dimensional geometric shape that is perfectly round and smooth, much like a ball. It is a commonly encountered shape in everyday life, and is used in fields ranging from science and engineering to art and design. The volume of a sphere is a fundamental calculation that is used in many applications, such as in determining the capacity of a container or the size of a planet.
The formula for the volume of a sphere is given by:
V = (4/3) * π * r^3
where V is the volume, π is the mathematical constant pi (approximately equal to 3.14159), and r is the radius of the sphere.
To find the volume of a sphere, you simply need to plug in the radius value into the formula and perform the necessary calculations. Let’s look at an example:
Example: Find the volume of a sphere with a radius of 5 units.
Solution: Using the formula for the volume of a sphere, we can plug in the value of the radius and calculate as follows:
V = (4/3) * π * r^3 V = (4/3) * π * 5^3 V = (4/3) * π * 125 V = 523.6 cubic units
Therefore, the volume of the sphere with a radius of 5 units is approximately 523.6 cubic units.
It is important to note that the units of measurement used for the radius will determine the units of measurement for the volume. For example, if the radius is measured in meters, the volume will be in cubic meters.
Here are some questions with their answers related to the volume of a sphere:
What is the formula for the volume of a sphere? Answer: The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.
What is the volume of a sphere with a radius of 5 cm? Answer: Using the formula, V = (4/3)πr^3, and substituting r=5, we get V = (4/3)π(5^3) = 523.6 cubic centimeters (rounded to one decimal place).
A spherical water tank has a radius of 3 meters. What is the volume of water it can hold? Answer: Using the formula, V = (4/3)πr^3, and substituting r=3, we get V = (4/3)π(3^3) = 113.1 cubic meters (rounded to one decimal place). Therefore, the water tank can hold 113.1 cubic meters of water.
A metal ball has a volume of 288π cubic centimeters. What is its radius? Answer: Using the formula, V = (4/3)πr^3, and substituting V=288π, we get 288π = (4/3)πr^3. Solving for r, we get r = (3*288π/4π)^(1/3) = 6 centimeters (rounded to one decimal place).
If the volume of two spheres are in the ratio 27:64, what is the ratio of their radii? Answer: Let the radii of the spheres be r1 and r2, and their volumes be V1 and V2 respectively. We know that V1/V2 = 27/64. Using the formula, V = (4/3)πr^3, we can write V1/V2 = (r1/r2)^3. Substituting V1/V2 = 27/64, we get (r1/r2)^3 = 27/64. Solving for r1/r2, we get r1/r2 = 3/4. Therefore, the ratio of their radii is 3:4.
In conclusion, the volume of a sphere is an important calculation that can be easily determined using the formula V = (4/3) * π * r^3. This formula can be used to solve a variety of problems related to spheres in different fields.
