# Volume of the Hemisphere

## The volume of the hemisphere

Hemisphere shapes are commonly found in everyday items like bowls, mushrooms, hats, cakes, and headphones. Geographically, an imaginary line known as the equator divides the Earth into two hemispheres: the northern and southern hemispheres.

When we talk about the volume of a shape, it's calculated by multiplying the area of its base by its height. For a hemisphere, which is half of a sphere, the volume can be expressed as:

V=πr 3

## How to Find the Volume of a Hemisphere?

To calculate the volume of a hemisphere, we use the formula:

**Volume of hemisphere = (2/3)πr ^{3}**

Let's find the volume of a hemisphere with a radius of 14 units:

**Step 1:**Note down the radius of the hemisphere. Here, the radius (r) = 14 units.**Step 2:**Substitute the radius value into the formula for the volume of a hemisphere,**Volume = (2/3)πr**, and express the final answer in cubic units.^{3}**Step 3:**After substituting*r = 14*, calculate the volume:

Volume = (2/3)π × 14^{3}

Volume = (2/3)π × 2744

Volume ≈ 5749.33 cubic units

Therefore, the volume of the hemisphere with a radius of 14 units is approximately 5749.33 cubic units.

Hemisphere volume

### Hemisphere Capacity

Hemisphere shapes are frequently encountered in daily life, seen in items like dishes, mushrooms, hats, cakes, and headphones. Geographically, the equator acts as an imaginary line dividing the Earth into two halves known as the northern hemisphere and the southern hemisphere.

When it comes to calculating the volume of a hemisphere, the formula for its capacity is given by V = 2/3πr³, where 'r' represents the radius of the hemisphere. This formula utilizes the concept that the volume of any upright structure can be determined by multiplying its base area by its height.

The volume of any standing position is its base × its height. Hemisphere

capacity is provided:

V = 2 / 3πr3

### How Can You Find the Equatorial Volume?

The volume of a hemisphere can be calculated using the formula:

**Volume of Hemisphere** = *2πr ^{3} / 3*

Let's find the volume of a hemisphere with a radius of 14 units.

**Step 1: **Identify the radius of the hemisphere. In this case, the radius (r) is 14 units.

**Step 2:** Substitute the radius value into the volume formula. The formula is:

**Volume of Hemisphere** = *2πr ^{3} / 3*

**Step 3:** Plug in the radius (r = 14) into the formula and calculate the volume.

**Volume of Hemisphere** = *2π(14) ^{3} / 3*

Breaking it down further:

(14)^{3} = 14 × 14 × 14 = 2744

Then:

**Volume of Hemisphere** = *2π × 2744 / 3*

Using π ≈ 22/7:

**Volume of Hemisphere** = *2 × 22/7 × 2744 / 3*

**Volume of Hemisphere** = *2 × 22 × 2744 / 21*

**Volume of Hemisphere** = 120,768 / 21

**Volume of Hemisphere** ≈ 5749.33 cubic units

So, the volume of a hemisphere with a radius of 14 units is approximately 5749.33 cubic units.

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## Frequently Asked Questions on Volume of the Hemisphere

A hemisphere is a half of a sphere, or a 3D geometric shape that is formed by cutting a sphere exactly in half along its diameter. The most common examples are the northern and southern hemispheres of the Earth.

The total surface area of a hemisphere is the sum of its curved surface area and the area of its flat base. The curved surface area is half the surface area of a sphere with the same radius, while the base area is the area of a circle with the same radius.

The volume of a hemisphere is calculated as one-half the volume of a sphere with the same radius. The formula for the volume of a hemisphere is: V = (2/3) × π × r^3, where r is the radius of the hemisphere.

The law of volume of a hemisphere states that the volume of a hemisphere is equal to two-thirds of the volume of the sphere with the same radius. This relationship is expressed in the formula: V = (2/3) × π × r^3.

The key formulas for hemispheres include:

- Curved surface area: A = 2πr^2
- Base area: A = πr^2
- Total surface area: A = 3πr^2
- Volume: V = (2/3)πr^3.