The volume of a sphere determines its capacity. If a sphere is split into two halves, the volume will be the internal space or the material filled inside. If there is an empty space inside the sphere, it is hollow. If the filler material is present, the sphere will be solid. The volume of sphere formula that is used to compute the volume of a sphere mathematically is equal to r^{3}, where r is the radius of the sphere.
Volume of a Cone
Cone is a three-dimensional solid object with a smooth transition from a circular base to a point termed the vertex in geometry. The height of the cone is perpendicular to the base and is measured from the vertex to the base. The volume of a cone is the amount of space it occupies and it’s measured in cubic units.
The volume of the cone= *(Area of base) * height
Volume of the cone = ℼ r^{2 }h |
What is the Volume of Sphere Formula?
The volume of a sphere is the amount of space it takes up within it. The sphere is a three-dimensional circular solid form with equal spacing between all points on its surface. The radius of a sphere is its fixed distance, while the centre is its fixed point. The three coordinates x, y, and z determine the volume of a sphere. Because a three-dimensional object has three perpendicular axes. Cubic meters, cubic feet, cubic inches, and other comparable units are used to measure volume. The symbols cm^{3}, m^{3}, in^{3}, and so on are used to represent it.
The derivative of the volume of a sphere derives from the division of the volume of a cone, sphere, and cylinder of the same cross-sectional area into slices, which led to the conclusion that the volume of a cone and sphere is equal to the volume of a cylinder of the same cross-sectional area. The volumes are in the following proportions: 1:2:3.
∴ The Volume of Sphere = π r^{3} |
Procedure to Calculate Volume of Sphere
Follow the steps given below to calculate the volume of the sphere
- Study the data in the question carefully.
- Check the value of radius. If the diameter is given calculate radius by dividing the diameter by 2 and if the circumference is given, find the radius from the formula 2𝜋r.
- Check the units. Convert all equivalent units into a single form.
- Calculate the cube of the radius, i.e., r3.
- Now multiply the value of r³ by 𝜋.
- Multiply the value found in Step 5 by 4/3.
- The final value you get is the volume of a sphere.
Real-Life Application of the Volume of a Sphere Formula
The balls used in sports like football, basketball, volleyball etc are nothing more than spheres of various radii. The capacity or volume of such spherical objects can be calculated using the volume of a sphere formula. If you know the radius of a sphere, you can easily calculate its volume.
Examples
Example1. Calculate the volume of a sphere whose radius is 4 cm?
Solution:
Given: Radius, r = 4 cm
V = × 3.14 ×( 4)^{3}
V = × 3.14 × 4 × 4 ×4
V = 267.94 cm^{3}
∴ Volume of the radius is 267.94 cm^{3}
Example 2: The Volume of a sphere is 3600 cm^{3}. Find the radius of the sphere.
Solution:
Given Volume = 3600cm^{3}
Now the formula for Volume of sphere = π r^{3}
∴ 3600= π r^{3}
r^{3} =
r =
r = 9.512 cm
∴Radius of the sphere is 9.512 cm
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