Cylinder Calculator
The cylinder is a three dimensional solid having two parallel circles of the same radii on top and bottom and two vertical lines that join those circles. The center of circular bases overlaps each other to form a right cylinder. The line segment joining those two centers is the axis, that denotes the height of a cylinder.
radius | r = |
height | h = |
volume | V = |
lateral surface area | L = |
top surface area | T = |
base surface area | B = |
total surface area | A = |
In Terms of Pi π | |
volume | V = |
lateral surface area | L = |
top surface area | T = |
base surface area | B = |
total surface area | A = |
Formulas of Circular Cylinder
This page not only provides the solution for circular cylinder problems but also provides the formulas to calculate the cylinder measurements. Get the formulas that are useful to compute the cylinder height, radius, volume, total surface. Utilize these formulas whenever required to solve the questions effortlessly.
- The Volume of a Cylinder Formula:
- Volume V = πr²h
- Lateral Surface Area of a Cylinder Formula:
- Lateral Surface Area L = 2πrh
- Top and Bottom Surface Area of Cylinder Formula:
- Top Surface Area T = πr²
- Bottom Surface Area B = πr²
- Total Surface Area of a Cylinder formula:
- Total Surface Area A = L + T + B = 2πrh + 2(πr²) = 2πr(h+r)
- Circumference of a Circular Cylinder Formula:
- Circumference C = 2πr
Cylinder Calculations
This section contains the additional formulas of a circular cylinder which are helpful to solve any type of questions.
- If the cylinder height, volume are given, then
- Radius r = √( V / πh )
- Lateral Surface Area L = 2πh√(V / πh)
- Circumference C = 2π√(V / πh)
- Top and Bottom Surface Area = T = B = (V / h)
- Total Surface Area A = L + T + B = 2πh√(V / πh) + (V / h)
- If height, the lateral surface area of the cylinder are given, then
- Radius r = L / 2πh
- Circumference C = L / h
- Volume V = L² / 4πh
- Top and Bottom Surface Area = T = B = L² / 4πh²
- Total Surface Area A = L + T + B = L + 2(L² / 4πh²)
- If the lateral surface area, the radius of the cylinder are given, then
- Height h = L / 2πr
- Circumference C = L
- Top and Bottom Surface Area = T = B = L² / 4π
- Total Surface Area A = L + T + B = L + L² / 2π
- Volume V = (L² * h) / 4πr²
- If the radius, volume of the circular cylinder are given, then
- Height h = V / πr²
- Lateral Surface Area L = 2πrh
- Top Surface Area T = πr²
- Bottom Surface Area B = πr²
- Total Surface Area A = L + T + B = 2πrh + 2(πr²)
- Circumference C = 2πr
- If the height, radius of the cylinder are known, then
- Volume V = πr²h
- Lateral Surface Area L = 2πrh
- Top Surface Area T = πr²
- Bottom Surface Area B = πr²
- Total Surface Area A = L + T + B = 2πr(h+r)
- Circumference C = 2πr
Where, r is the radius
h is the cylinder height
V is volume
L is the lateral surface area
T is the top surface area
B is the base surface area
A is the total surface area of the cylinder
C is circle circumference
Steps to Get Cylinder Volume, Surface Area, Height
Check out the following instructions while computing the unknown measures of a circular cylinder. You will learn the detailed process to solve the circular cylinder radius, height, volume, lateral surface area, top, bottom, and total surface area easily. The steps are along the lines:
Circular Cylinder Volume:
- Check the radius, height of the cylinder.
- Square the radius and multiply it with π, height.
- The obtained value is volume.
Circular Cylinder Lateral Surface Area:
- Get cylinder height, radius.
- Double the radius and multiply it with π, height.
- The result is called the lateral surface area.
Circular Cylinder Top, Bottom Surface Area:
- Make a note of the radius, height.
- Multiply π with the square of radius to get the top surface area.
- The top and bottom surface areas are same.
Circular Cylinder Total Surface Area:
- Either add lateral, top, and bottom surface areas.
- Or add height and radius of the cylinder.
- Multiply the sum with double radius and π.
Cylinder Circumference:
- Check the radius of the cylinder from the question.
- Find the product of π, twice of radius to get the circumference.
Cylinder Height:
- Process 1:
- Note down the volume, radius of the circular cylinder.
- Multiply the square of the radius with π.
- divide the volume by the product to check the height of a cylinder.
- Process 2:
- Find out lateral surface area, radius.
- Divide the lateral surface area by double-radius and multiple with π.
Circular Cylinder Radius:
- Process 1:
- Get the product of double height and π.
- Divide the lateral surface area by product to get the radius.
- Process 2:
- Make a note of the volume, and cylinder height.
- Divide the volume by π times of height.
- Apply square root to the result to get the radius.
Solved Examples on Cylinder
Example 1: Compute the circular cylinder height, volume, circumference, top surface area, base surface area, and total surface area? The cylinder radius is 5 cm, the lateral surface area is 314 cm².
Solution:
Given that,
Cylinder radius r = 5 cm
Lateral surface area L = 314 cm²
Height h = L / 2πr
= 314 / 31.4 = 10 cm
Circumference C = L
C = 10 cm
Top and Bottom Surface Area = T = B = L² / 4π
= 314² / 4π
= (314 * 314) / (4 * 3.14)
= 98,596 / 12.56 = 7,850 cm²
Total Surface Area A = L + T + B = L + L² / 2π
A = 314 + 314² / 2π
= 314 + (314 * 314) / (2 * 3.14)
= 314 + 98,596 / 6.28 = 314 + 15,700
= 16,014 cm²
Volume V = (L² * h) / 4πr²
V = (314² * 10) / (4 * 3.14 * 5²)
= (314 * 314 * 10) / (4 * 3.14 * 5 * 5)
= (98,596 * 10) / (314)
= 985960 / 314 = 3,140 cm³
∴ Circular Cylinder volume is 3,140 cm³, total surface area is 16,014 cm², top, base surface area is 7,850 cm², circumference is 10 cm, lateral surface area is 314 cm², height is 10 cm, and radius is 5 cm.
Example 2: If the cylinder radius is 9 m, and the volume is 6,104 m³. Find the cylinder height, lateral surface area, top, base surface area, total surface area, and circumference.
Solution:
Given that,
The radius of the cylinder r = 9 m
Volume V = 6,104 m³
Height h = V / πr²
h = 6,104 / ( 3.14 * 9²)
= 6,104 / ( 3.14 * 9 * 9)
= 6,104 / (254.34)
= 23.9 m
Lateral Surface Area L = 2πrh
L = 2 * 3.14 * 23.9
= 150.092 m²
Top Surface Area T = πr²
= 3.14 * 9²
= 3.14 * 9 * 9 = 254.34 m²
Bottom Surface Area B = πr²
= 3.14 * 9² = 254.34 m²
Total Surface Area A = L + T + B = 2πrh + 2(πr²)
A = 2πrh + 2(πr²)
= 2 * 3.14 * 9 * 23.9 + 2(3.14 * 9²)
= 1,350.828 + 2(254.34)
= 1,350.828 + 508.68 = 1,859.508 m²
Circumference C = 2πr
C = 2 * 3.14 * 9
= 56.52 m
∴ Circular Cylinder radius is 9 m, height is 23.99 m, the volume is 6,104 m³, the total surface area is 1,859.508 m², top, the base surface area is 254.34 m², circumference is 56.52 m, the lateral surface area is 150.092 m².
Areavolumecalculator.com has got comprehensive array of calculators for geometry concepts all at one place.
FAQs on Cylinder Calculator
1. What is the formula for finding the surface area of a cylinder?
To get the total surface area of a cylinder, you must calculate the lateral surface area and top, base surface area. Circular cylinder total surface area formula is A = 2πr(h+r). Here r is the radius, and h is the height.
2. How do you find the diameter of a cylinder?
The formula to compute the cylinder volume V = πr²h
Divide both sides of the equation by πh
(V / πh) = πr²h / πh
V / πh = r²
Apply square root to both sides.
r = √V / πh
As the diameter is double the radius
d = 2 * √V / πh
3. What is the definition of a cylinder?
A cylinder is a three-dimensional shaped object consisting of two parallel circular bases joined by a curved surface. The center of the circular base overlaps each other to form a right cylinder. the line segment joining two centers is the axis, called the height.
4. What are the properties of the cylinder?
Cylinder properties are mentioned here.
- Bases are always congruent and parallel.
- If the axis forms a right angle with bases, which are exactly over each other, then it is the right cylinder.
- If bases are in a circular shape, then it is right circular cylinder.
- If the bases are in an elliptical shape, then it is an elliptical cylinder.