Hemisphere Calculator

The hemisphere calculator helps you to find the different properties of hemisphere from any 1 known variables. Also, this online tool calculates the variables in terms of Pi (ᴨ). The calculator allows you to determine the variables from the following known variable.

• Radius.
• Total surface area.
• Volume.
• Curved surface area.
• Base circumference.

By using this Hemisphere calculator, you will be able to calculate the volume of a hemisphere as well as the surface area of a hemisphere with the circumference of the base. Read on!

Hemisphere Formulas:

As it is the sphere divided into two halves, so its calculations is the same as the calculations for the sphere just divided by two.

• The formula used by this volume of a hemisphere calculator is as follows:

$$ V = \frac{2}{3}\pi r^3 $$

• The formula for the circumference of base is:

$$ C = 2 \pi r $$

• The formula for curved surface area is:

$$ A = 2 \pi r^2 $$

• The formula for the calculation of the base area of a hemisphere:

$$ B = \pi r^2 $$

• Total surface area of the hemisphere can be calculated by the following formula:

$$ K = 3 \pi r^2 $$

How to do the Hemisphere Calculations Manually:

Given V, Find r, A, C, K:

When the volume given, calculate the radius, curved surface area, circumference and total surface area with the following formula: $$ r = \text {cube root}\frac{3V}{2\pi} $$

Example:

The volume is 35ft3, find the radius, curved surface area, total surface area and circumference of the half circle?

Solution:

The formula used by this calculation is:

$$ r = \text {cube root}\frac{3V}{2\pi} $$

$$ r = \text {cube root}\frac{3(35)}{2(3.14)} $$

$$ r = \text {cube root}\frac{105}{6.28} $$

$$ r = \text {cube root}(16.71) $$

$$ r = \text 2.55ft $$

To calculate curved surface area:

$$ A = 2 \pi r^2 $$

$$ A = 2 (3.14) (2.55)^2 $$

$$ A = 2 (3.14) (6.50) $$

$$ A = 41.08 ft^2 $$

Now, the total surface area of hemisphere can be calculated from the following formula:

$$ K = 3 \pi r^2 $$

$$ K = 3 (3.14) (2.55)^2 $$

$$ K = 3 (3.14) (6.50) $$

$$ K = 61.62 ft^2 $$

Now, use the formula for circumference to calculate it:

$$ C = 2 \pi r $$

$$ C = 2 (3.14) (2.55) $$

$$ C = 16.04 ft $$

Given A, Find r, V, C, K:

When the curved surface given, calculate the radius, volume, circumference and total surface area with the following formula: $$ r = \sqrt {(\frac{A}{2\pi})} $$

Example:

If the curved surface area is 46ft2, find the radius, volume, circumference & total surface area?

Solution:

The formula used to calculate radius from the above scenario is:

$$ r = \sqrt {(\frac{A}{2\pi})} $$

$$ r = \sqrt {(\frac{46}{2 (3.14)})} $$

$$ r = \sqrt {(\frac{46}{6.28})} $$

$$ r = \sqrt {7.32} $$

$$ r = 2.70 $$

To find volume of a hemisphere, the calculator uses the following formula:

$$ V = \frac{2}{3}\pi r^3 $$

$$ V = \frac{2}{3}(3.14) (2.70)^3 $$

$$ V = \frac{2}{3}(3.14) (19.68) $$

$$ V = \frac{2}{3}(61.80) $$

$$ V = \frac{123.60}{3}  $$

$$ V = 41.49 ft^3  $$

For calculation of circumference,

$$ C = 2 \pi r $$

$$ C = 2 (3.14) (2.70) $$

$$ C = 17 ft $$

Now, total surface area is calculated as:

$$ K = 3 \pi r^2 $$

$$ K = 3 (3.14) (2.70)^2 $$

$$ K = 3 (3.14) (7.29) $$

$$ K = 69 ft^2 $$

Given K, Find r, V, A, C:

When the total surface area given, calculate the radius, volume, curved surface area and circumference with the following formula: $$ r = \sqrt {(\frac{K}{3\pi})} $$

Example:

The total surface area is 85ft2, then find out the radius & other different variables related to hemisphere?

Solution:

To calculate the radius,

$$ r = \sqrt {(\frac{K}{3\pi})} $$

$$ r = \sqrt {(\frac{85}{3(3.14)})} $$

$$ r = \sqrt {(\frac{85}{9.42})} $$

$$ r = \sqrt {9.02} $$

$$ r = 3 ft $$

To find the volume of hemisphere,

$$ V = \frac{2}{3}\pi r^3 $$

$$ V = \frac{2}{3} (3.14) (3)^3 $$

$$ V = \frac{2}{3} (3.14) (27) $$

$$ V = \frac{2}{3} (84.78) $$

$$ V = \frac{169.56}{3} $$

$$ V = 56.71 ft^3 $$

For the calculation of curved surface area,

$$ A = 2 \pi r^2 $$

$$ A = 2 (3.14) (3)^2 $$

$$ A = 2 (3.14) (9) $$

$$ A = 56.62 ft^2 $$

Now, the circumference is:

$$ C = 2 \pi r $$

$$ C = 2 (3.14) (3) $$

$$ C = 18.86 ft $$

Given C, Find r, V, A, K:

When the circumference is given, calculate the radius, volume, curved surface area and total surface area with the following formula: $$ r = \frac {C}{2(\pi)} $$

Example:

The circumference of the half circle is 25ft; find the radius, volume, curved surface area & total surface area of the hemisphere?

Solution:

To calculate the radius,

$$ r = \frac {C}{2(\pi)} $$

$$ r = \frac {25}{2(3.14)} $$

$$ r = \frac {25}{6.28} $$

$$ r = 3.979ft $$

Now, to find the volume:

$$ V = \frac{2}{3}\pi r^3 $$

$$ V = \frac{2}{3}(3.14) (3.979)^3 $$

$$ V = \frac{2}{3}(3.14) (62.99) $$

$$ V = \frac{2}{3}(197.78) $$

$$ V = \frac{395.56}{3} $$

$$ V = 131.94 ft^3 $$

The area of the curved surface is,

$$ A = 2 \pi r^2 $$

$$ A = 2 (3.14) (3.979)^2 $$

$$ A = 2 (3.14) (15.83) $$

$$ A = 99.47 ft^2 $$

The total surface area of the hemisphere is:

$$ K = 3 \pi r^2 $$

$$ K = 3 (3.14) (3.979)^2 $$

$$ K = 3 (3.14) (15.83) $$

$$ K = 149.217ft^2 $$

Frequently Ask Questions (FAQ’s):

What is a hemisphere?

When a plane passes through the centre or origin of the sphere & dividing it into two halves, then two half circles are created each is known as hemisphere. It includes the surface area of a curved surface as well as the area of base. As the hemisphere is half of the circle, so its volume is half of the volume of the sphere of corresponding radius.

What is the TSA of the sphere?

A sphere is three-dimensional solid with a round shape, like circle. Total surface area (TSA) of a sphere can be found as: $$ Surface Area= 4 \pi r^2 $$

How do you find the diameter of a hemisphere?

The basic formula to calculate the diameter of the half circle is: $$ d= 2r $$ First of all, r is calculated according to the above mentioned calculation method with different known parameters.

Why is it called Hemisphere?

The word comes from the Greek language and combines with the hemi prefix which means “half”. So, it means “the half of the sphere”. The Earth is divided into northern & Southern hemispheres.

References:

From the source of Wikipedia: Hemisphere, As half of the Earth, As half of the brain, and other. From the source of nationalgeographic: All you need to explore about hemispheres The site ck12 provides: Spheres and Hemi-spheres: Surface Area and Volume (ultimate and simple guide)