Hemisphere Total Surface Area

We need to know the total surface area of a hemisphere or even any shape. It allows us to get an insight into the object’s capability to interact with different forms like solid, liquid, and gas. The more surface area an object covers, the smaller its particles are, and it can interact with more forms of matter and derive multiple purposes of scientific importance. In this guide below, we will try to learn how to calculate the total surface area of a hemisphere and possibly the various effects it has on science and other purposes.

The Formula

Solid and Hollow hemisphere

The total surface area of a hemisphere formula depends on the type of hemisphere it is. It has various uses in the field of mathematics and science to conduct various thesis analyses and understand graphs and other models smoothly.

Two types of hemispheres are available, namely hollow and solid. We are going to talk about them in the section below.

Total surface area (TSA) of a solid hemisphere

A solid hemisphere has more mass, density and has much more particles. Hence, we must consider all of these factors when calculating the total surface area. A solid hemisphere has two parts. The curved area of the semi-circle and the flat area on top are also known as the base area. So the total surface area of a hemisphere is simply 3πr², where r² is the radius of the base + the curve.

The Curved surface area has to account for the curvature of the semicircle, and hence the value of π² has to be doubled. Hence it is calculated as 2πr².

The flat or base surface area is just the consideration of circumference and diameter, so it is simply considered as πr²

So the total surface area of a hemisphere formula is concluded as 2πr²+πr² = 3πr².

The total surface area of a hollow hemisphere

A hollow hemisphere is simply a bowl form of a hemisphere. If it can hold water, solids, or any material on its curved surface, it is considered a hollow hemisphere. Naturally, there are now two types of radius considerations to be used.

The first radius is that of the inner circle, which is hollow. The second radius is that of the rim of the semi-circle, which is solid.

If R is the radius of the hollow part of the hemisphere &

r is the radius of the solid part of the hemisphere

so the TSA of the hollow inner circle will be 2πR²

And the TSA of the solid rim of the circle will be 2πr²

The third consideration is the area between the hollow and the solid part of the hemisphere. This is calculated as π(R²-r²)

So, the total surface area of the hollow hemisphere is calculated as

TSA of hollow inner circle + TSA of the solid rim of circle + area between hollow and solid

  [2πR²]                                [2πr²]                                   [π(R²-r²)

]

2πR²+2πr²+π(R²-r²) = 3πR² + πr²

So once again, the total surface area of the hollow hemisphere = 3πR² + πr²

Components of the total surface area of hemisphere formula

There are majorly three components of the total surface area of the hemisphere formula.

1. π – Also known as Pi, it is calculated as 

Circumference of circle ⁄ Diameter of the circle

This ratio is always equal to Pi or 3.14 for any circle size. This never changes for any circle, no matter how small or big.

1. R or r – This is the radius of a circle. It is simply the distance from the center of a circle to the ring of the same circle. Without the radius, it is impossible to know the volume, surface area.
2. Shape – The shape of the hemisphere considers if it is hollow or solid.

Conclusion :

The total surface area of a hemisphere can determine the speed, strength, curvature, capacity to hold matter, and interaction power with other sphere materials. Irrespective of the material with which the sphere is made up, the total surface area of a hemisphere formula assists many scientists and mathematicians worldwide to come up with various surface area analyses and results that assist with a lot of scientific improvements and discoveries around the world. This formula is applied to pharmaceuticals, catalysts, area metrics, and matter composition and fluidity. The solubility of a product, the chemical reaction time and energy consumed, the collision of particles, size distribution, gas absorption, ingredient calculation, and measure are all big components of hemisphere calculation that have benefitted the scientific community for many ages.