Volume of Sphere

Volume

When we think about how much water our bottle can hold, that's where we are talking about the volume of an object. Mathematically, volume is the amount of space an object occupies. For shapes like spheres and hemispheres, we need special formulas to calculate their volumes. Knowing volume matters for many reasons. Engineers design efficient containers using volume calculations. Physicists study volumes to learn about matter.

What are Spheres?

What will the shape of a basketball be? At first, we will think it is a circle, but it is not. The basketball is spherical. Mathematically, a sphere is a three-dimensional round-shaped object. In this article, we will get to know the formula for calculating the volume of the sphere and do some examples to understand the concept.

Volume of Sphere

Now, we have understood the basic terms like volume and sphere. So it will be easy for us to understand the volume of a sphere. The formula for the volume of the sphere is:
V = $\frac{\frac{4}{}}{\frac{3}{}}$πr³.
Where,
V denotes the volume of the sphere
r denotes the radius of the sphere.
Π (pi) is a symbol in math that has a value of approximately 3.14159.

The above equation tells us how much space fits inside the sphere's boundaries. A sphere is simply shaped, but measuring its volume requires an exact formula.

Click Here to Read About: Volume of Hemisphere

What are Hemispheres?

If we cut a ball midway, we will get a hemisphere. Mathematically, the definition of the hemisphere is “A hemisphere is a 3D object that is half of a sphere, with one side being flat and the other being a bowl-like shape.”

Volume of a Hemisphere

To find the volume of a hemisphere, we just need to do one small thing, multiply by ½ with the volume of a sphere. That means the volume of the hemisphere is half the volume of the sphere. The formula is:
V = $\frac{\frac{2}{}}{\frac{3}{}}$πr³,
where,
V represents the volume of the hemisphere
r represents the radius of the hemisphere

Solved Questions of the Volume of Sphere

1. What is the volume of a sphere with a radius of 7 units?

Solution: Given: Radius (r) = 7 units
Using the formula for the volume of a sphere: V = $\frac{\frac{4}{}}{\frac{3}{}}$πr³
Substituting the values, we get
V = $\frac{\frac{4}{}}{\frac{3}{}}$ × π × (7)³
V = $\frac{\frac{4}{}}{\frac{3}{}}$ ×$\frac{\frac{\mathrm{22}}{}}{\frac{7}{}}$ × 343 (since π = $\frac{\frac{\mathrm{22}}{}}{\frac{7}{}}$)
V = 1437.34 cubic units

Hence, the volume of the sphere is 1437.34 cubic units.

2. If the volume of a sphere is 972π cubic inches, what is its radius?

Solution: Given: Volume (V) = 972π cubic inches
We know the formula for the volume of a sphere: V = $\frac{\frac{4}{}}{\frac{3}{}}$πr³
Let's substitute V = 972π in the formula and we will get
972π = $\frac{\frac{4}{}}{\frac{3}{}}$πr³
972 = $\frac{\frac{4}{}}{\frac{3}{}}$r³ (cancelling out π)
r³ = 972 × $\frac{\frac{3}{}}{\frac{4}{}}$
r³= 729
Taking the cube root of both sides: r = ³√729
r = 9 inches

Hence, the radius of the sphere is 9 inches.

3. If the volume of a sphere is 2304π cubic centimetres, what is its diameter?

Solution: Given: Volume (V) = 2304π cubic centimetres
We know the formula for the volume of a sphere: V = $\frac{\frac{4}{}}{\frac{3}{}}$πr³
We need to find the radius (r) first.
2304π = $\frac{\frac{4}{}}{\frac{3}{}}$πr³
r³ = 2304 × $\frac{\frac{3}{}}{\frac{4}{}}$
r³ = 1728
r = ³√1728
r = 12 cm
Now that we have the radius, we can find the diameter (d) using d = 2r
d = 2 x 12 = 24 cm

Hence, the diameter of the sphere is 24 cm

Frequently Asked Questions

1. How do you find the volume of a sphere if only the diameter is given?

Answer: If the diameter (d) of a sphere is given, you can first find the radius (r) using r = $\frac{\frac{d}{}}{\frac{2}{}}$, and then use the formula $\frac{\frac{4}{}}{\frac{3}{}}$πr³ to find the volume.

2. What are the common units used for measuring the volume of a sphere?

Answer: The volume of a sphere is commonly measured in cubic units such as cubic centimetres (cm³), cubic inches (in³) or cubic metres (m³).

3. How to calculate the volume of a hemisphere?

Answer: The volume of a hemisphere, which is half of a sphere, can be calculated using the formula,
V = $\frac{2}{3}\pi r^3$, where r is the radius of the hemisphere.