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Hemisphere Surface Area Calculator

Introduction

Welcome to our nifty Hemisphere Surface Area Calculator, which will help you calculate the Surface Area of the Hemisphere with ease. The hemisphere is a solid three-dimensional shape, and it is formed when a sphere is cut into two equal halves, giving us two hemispheres. The hemisphere has one flat surface and a curved surface in a bowl shape. Some real-life examples of hemispheres include lemons cut in half, giving us two hemispheres; Similarly, a bowl with its open side on a table gives us a hemisphere.

The lateral surface area of the hemisphere is covered by its curved surface in three-dimensional space. So, the total surface area of the hemisphere is the sum of the lateral surface area and the area of the base of the hemisphere.

How to use Hemisphere Surface Area Calculator?

Using the hemisphere surface area calculator, you can calculate the lateral surface area and also the hemisphere’s total surface area by inputting the hemisphere’s radius.

The variables in the Hemisphere Surface Area Calculator include

Radius (r) The distance between the center of the base to any point on the circumference of the base.

Lateral Surface Area (LSA) The area is covered by the sphere’s curved surface in three-dimensional space.

Total Surface Area (TSA) The sum of the curved surface and the area of the base of the hemisphere.

How is the Lateral Surface Area of the Hemisphere Calculated?

The lateral surface area of the hemisphere is the area of the curved surface of the hemisphere.

We can calculate the lateral surface area of the hemisphere by using the following formula.

LSA=2πr2\text{LSA} = 2 \pi r^2

Where

r = radius of the hemisphere

How is the Total Surface Area of the Hemisphere Calculated?

The total surface area of the hemisphere is the area of the curved surface of the hemisphere and also the area of the base of the hemisphere.

We can calculate the total surface area of the hemisphere by using the following formula.

TSA=2πr2+πr2=3πr2\begin{aligned} \text{TSA} &= 2 \pi r^2 + \pi r^2 \\[10pt] &= 3 \pi r^2 \end{aligned}

Where,

r = radius of the hemisphere

Examples

Given a hemisphere with a radius of 7 cm. What are the lateral surface area and the total surface area of the hemisphere?

We can calculate the lateral surface area of the hemisphere using the following formula

LSA=2πr2=2⋅π⋅72=307.87  cm2\begin{aligned} \text{LSA} &= 2 \pi r^2 \\[10pt] &= 2 \cdot \pi \cdot7^2 \\[10pt] &= 307.87 \; cm^2 \end{aligned}

we can calculate the total surface area of the hemisphere using the following formula

TSA=3πr2=3⋅π⋅72=461.81  cm2 \begin{aligned} \text{TSA} &= 3 \pi r^2 \\[10pt] &= 3 \cdot \pi \cdot 7^2 \\[10pt] &= 461.81 \; cm^2 \end{aligned}
Author

hexacalculator design team

Our team blends expertise in mathematics, finance, engineering, physics, and statistics to create advanced, user-friendly calculators. We ensure accuracy, robustness, and simplicity, catering to professionals, students, and enthusiasts. Our diverse skills make complex calculations accessible and reliable for all users.

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