Hemisphere Calculator
In geometry, the hemisphere is defined as half of the sphere. Actually, the word Hemi means half, and sphere is a three-dimensional object which is perfectly round like a basketball.
radius | r = |
base circumference | C = |
volume | V = |
curved surface area | A = |
base surface area | B = |
total surface area | K = |
In Terms of Pi π | |
base circumference | C = |
volume | V = |
curved surface area | A = |
base surface area | B = |
total surface area | K = |
Hemisphere Formulas
In this section, we are giving few important formulas that are helpful to solve the hemisphere volume, curved surface area, base surface area, base circumference, and total surface area. By having knowledge of these formulas, you can easily solve any difficult questions easily.
- The Volume of a Hemisphere Formula:
- Volume V = (2/3)πr³
- Circumference of the base of a hemisphere formula:
- Circumference C = 2πr
- Curved Surface Area of a Hemisphere Formula:
- Curved Surface Area A = 2πr²
- Base Surface Area of a Hemisphere Formula:
- Base Surface Area B = πr²
- Total Surface Area of a Hemisphere Formula:
- Total Surface Area K = A + B = (2πr²) + (πr²) = 3πr²
Hemisphere Calculations:
- If the curved surface area of a hemisphere is given, then
- Radius r = √(A / 2π)
- Circumference C = √(A * 2π)
- Volume V = (2/3)πr³
- Base Surface Area B = A / 2
- Total Surface Area K = A + B = A + A / 2
- If the total surface area of a hemisphere is given, then
- Radius r = √(K / 3π)
- Curved Surface Area A = 2K / 3
- Base Surface Area B = K / 3
- Circumference C = 2π * √(K / 3π)
- Volume V = (2/3)π * [√(K / 3π)]³
- If the circumference of a hemisphere is known, then
- Radius r = C / 2π
- Volume V = (2/3)πr³
- Curved Surface Area A = 2πr²
- Base Surface Area B = πr²
- Total Surface Area K = A + B = (2πr²) + (πr²) = 3πr²
- If the volume of a hemisphere is given, then
- Radius r = Γê¢(3V / 2π)
- Base Surface Area B = πr²
- Curved Surface Area A = 2πr²
- Circumference C = 2πr
- Total Surface Area K = A + B = (2πr²) + (πr²) = 3πr²
Where,
r is the hemisphere radius
V is the volume
C is the circumference
A is the curved surface area
B is the base surface area
K is the total surface area
Steps to Calculate Surface Area, Volume of Hemisphere
Hemisphere is obtained by cutting the sphere into two equal parts. Each part is called a hemisphere. Look at the following steps and get the instructions, guidelines to compute the hemisphere radius, volume, surface area, and circumference. Make use of any of these steps to get the answer.
Hemisphere Base Circumference:
- Check the radius of the hemisphere.
- Double the radius, multiply it with π to get the circumference.
Hemisphere Curved Surface Area:
- Get the hemisphere radius from the question.
- Square the radius and multiply it with double of π.
- The obtained value is known as a curved surface area.
Hemisphere Volume:
- Make a note of the radius.
- Get the cube of radius, multiply it with π.
- Multiply the result by 2 and divide by 3 to find volume.
Hemisphere Base Surface Area:
- Find the hemisphere radius.
- Square the radius.
- Multiply the result with π to check the base surface area.
Hemisphere Radius:
- Process 1:
- Observe the hemisphere circumference.
- Divide the circumference by twice of π to get the radius.
- Process 2:
- Get the volume of a hemisphere.
- Divide three times of volume by 2 times of π.
- Apply the cube root to the result to check the radius.
- Process 3:
- Obtain total surface area.
- Divide the total surface area by three times of π.
- Apply square root to the answer to find the hemisphere radius.
- Process 4:
- Find out the hemisphere curved surface area value.
- Divide the curved surface area by twice of π.
- Square root of the result is the radius.
Hemisphere Total Surface Area:
- Note down hemisphere radius from the question.
- Calculate double of π, multiply it with radius square.
- Multiply the radius square with π.
- Add values from the above two steps to see the total surface area value.
Solved Examples on Hemisphere
Example 1: Hemisphere volume is 7,065 mm³. Find the hemisphere radius, circumference, base surface area, curved surface area, and total surface area?
Solution:
Given that,
Volume of the hemisphere V = 7,065 mm³
Hemipshere radius formula is r = Γê¢(3V / 2π)
r = Γê¢((3 * 7065) / (2 * 3.14))
= Γê¢(21195 / 6.28)
= Γê¢(3375) = 15 mm
Hemisphere Curved Surface Area A = 2πr²
A = 2 * 3.14 * 15²
= 6.28 * 225 = 1413 mm²
Hemisphere Base Surface Area formula is B = πr²
B = 3.14 * 15²
= 3.14 * 15 * 15
= 3.14 * 225 = 706.5 mm²
Circumference of a Hemisphere Formula is C = 2πr
C = 2 * 3.14 * 15
= 94.2 mm
Total Surface Area formula is K = A + B = (2πr²) + (πr²) = 3πr²
K = 1413 + 706.5
= 2,119.5 mm²
∴ Hemisphere radius is 15 mm, curved surface area is 1413 mm², base surface area is 706.5 mm², circumference is 94.2 mm, total surface area is 2,119.5 mm², and 7,065 mm³.
Example 2: If the hemisphere total surface area is 763 cm². Calculate the radius, curved surface area, circumference, base surface area, and volume of a hemisphere.
Solution:
Given that,
Total surface area of hemisphere K = 763 cm²
Hemisphere radius r = √(K / 3π)
r = √(763 / (3 * 3.14))
= √(763 / 9.42) = √80.99
= 8.9 cm
Hemisphere volume formula is V = (2/3)π(√(K / 3π))³
V = (2/3) * π * [√(763 / (3 * 3.14))]³
= (2/3) * π * [√(763 / 9.42)]³
= (2/3) * π * [√80.99]³
= (2/3) * π * [8.99]³
= (2/3) * π * 720.88 = 2π * 240.29
= 480.587π = 480.587 * 3.14
= 1,509.04 cm³
Circumference of a Hemisphere is C = 2π√(K / 3π)
= 2π√(763 / (3 * 3.14)
= 2π√(80.99) = 2 * 8.99 * π
= 17.98π = 17.98 * 3.14 = 56.457 cm
Hemisphere Curved Surface Area A = 2K / 3
A = (2 * 763) / 3
= 1526 / 3 = 508.66 cm²
Hemisphere Base Surface Area formula is B = K / 3
B = 763 / 2 = 381.5 cm²
∴ Hemisphere radius is 8.9 cm, base surface area is 381.5 cm², curved surface area is 508.66 cm², circumference is 56.457 cm, volume is 1,509.04 cm³, and total surface area is 763 cm².
Compute and understand geometry concepts in seconds by taking the help of free online tools provided at Areavolumecalculator.com.
Frequently Asked Questions on Hemisphere Calculator
1. What are the 4 hemispheres?
A circle drawn around the earth divides it into two equal parts called a hemisphere. In general, there are four hemispheres. They are northern hemisphere, eastern hemisphere, southern hemisphere, and western hemisphere.
2. What is the surface area of a hemisphere?
The total surface area of a hemisphere is the area covered by it. This is sum of the curved surface area and base area. Its formula is 3 times π of radius square. Mathematically, the hemisphere total surface area = 3π * radius².
3. What do you mean by the hemisphere?
A sphere is a three-dimensional shaped object where all the points lying on the surface is equidistant from the center. A hemisphere is formed when the plane cuts the sphere into two equal halves. A sphere is a combination of the two hemispheres.