Circle, Sphere, Cylinder Calculator
Calculator Use
Circle, Sphere, Cylinder Calculator is a free online tool that displays the Area, Perimeter or Volume of a Circle or Sphere or Cylinder. This online Circle, Sphere, Cylinder calculator tool performs the calculation faster, and it displays the result in a fraction of seconds.
The procedure to use the Circle, Sphere, Cylinder Calculator is as follows:
Step 1: Enter a values in the input field
Step 2: Now click the "What is this value" button to get the result
Step 3: Finally, The Area, Perimeter or Volume of a Circle, Sphere or Cylinder will be displayed in the output field
What is a Circle?
A circle closed plane geometric shape.
In technical terms, a circle is a locus of a point moving around a fixed point at a fixed distance away from the point.
Basically, a circle is a closed curve with its outer line equidistant from the center.
The fixed distance from the point is the radius of the circle.
How to calculate the Area of a circle?
The area of a circle is pi times the radius squared (A = π r²), or A = π d²/4.
Radius: The distance from the center to a point on the boundary is called the radius of a circle. It is represented by the letter 'r' or 'R'.
Diameter: A line that passes through the center and its endpoints lie on the circle is called the diameter of a circle. It is represented by the letter 'd' or 'D'.
Diameter formula: The diameter formula of a circle is twice its radius. Diameter = 2 × Radius
d = 2r or D = 2R
If the diameter of a circle is known, its radius can be calculated as:
r = d/2 or R = D/2
How to calculate the circumference of a circle?
The circumference of a circle is pi times the diameter (C = π d), or C = 2 π r.
Given the diameter d of a circle calculate the radius r, circumference C, area A(Given d calculate r, C, A)
r = d/2
C= 2 π r = 2 π d/2 = π d
A= π r² = π (d/2)² = π d²/4
Given the circumference C of a circle calculate the radius r, diameter d, area A(Given C calculate r, d, A)
r = C / 2π
d = 2 r = 2 C / 2π = C / π
A = π r² = π (C/2π)² = π C² / 4 π² = C² / 4 π
Given the area A of a circle calculate the radius r, diameter d, circumference C(Given A calculate r, d, C)
r = √(A/π)
d = 2 r = 2 √(A/π)
C = 2 π r = 2 π √(A/π)
What is a sphere?
A sphere is a three-dimensional round-shaped object.
A sphere does not have any edges or vertices, like other 3D shapes.
All the points on its surface are equidistant from its center. Hence, the distance from the center of the sphere to any point on the surface is equal. This distance is called the radius of the sphere.
A sphere has an only a curved surface, no flat surface, no edges and no vertices
Radius: The distance between surface and center of the sphere is called its radius
Diameter: The distance from one point to another point on the surface of the sphere, passing through the center, is called its diameter.
Surface area: The region occupied by the surface of the sphere is called it’s surface area
Volume: The amount of space occupied by any spherical object is called its volume
What is the Formulas for calculating the circumference,surface area and volume of a sphere?
Given the radius r of a sphere calculate the circumference C, surface area A and volume V (Given r calculate C, A, V)
Circumference of a sphere:
C = 2 π r
Surface area of a sphere:
A = 4 π r²
Volume of a sphere:
V = (4/3) π r3
Given the surface area A of a sphere calculate the radius r, circumference C and volume V (Given A calculate r, C, V)
Radius of a sphere:
r = √(A / 4π)
Circumference of a sphere:
C = √(A π)
Volume of a sphere:
V = A3/2 / (6 · √π)
Given the circumference C of a sphere calculate the radius r, surface area A and volume V (Given C calculate r, A, V)
Radius of a sphere:
r = C / 2π
Surface area of a sphere:
A = C² / 2
Volume of a sphere:
V = C3 / (6 · π²)
Given the volume V of a sphere calculate the radius r, circumference C and surface area A (Given V calculate r, C, A)
Radius of a sphere:
r = (3V / 4π)1/3
Circumference of a sphere:
C = π2/3 (6V)1/3
Surface area of a sphere:
A = π1/3 (6V)2/3
What are the Properties of a sphere?
A sphere is perfectly symmetrical
A sphere is not a polyhedron
All the points on the surface are equidistant from the center
A sphere does not have a surface of centers
A sphere has constant mean curvature
A sphere has a constant width and circumference.
What is a cylinder?
In mathematics, a cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.
These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis.
The perpendicular distance between the bases is the height, “h” and the distance from the axis to the outer surface is the radius “r” of the cylinder.
Cylinder is one of the basic 3d shapes, in geometry, which has two parallel circular bases at a distance.
The two circular bases are joined by a curved surface, at a fixed distance from the center.
The line segment joining the center of two circular bases is the axis of the cylinder. The distance between the two circular bases is called the height of the cylinder.
The top view of the cylinder looks like a circle and the side view of the cylinder looks like a rectangle.
Unlike cones, cube and cuboid, a cylinder does not have any vertices, since the cylinder has a curved shape and no straight lines. It has two circular faces.
What is the Formulas for calculating the surface area and volume of a cylinder?
Given the radius r and height h of a cylinder calculate the lateral surface area L, top and bottom surface area T and B , total surface area A and volume V (Given r, h calculate L, T, B, A, V)
Lateral surface area of a cylinder (just the curved outside):
L = 2 π r h
Top and bottom surface area of a cylinder (2 circles):
T = B = π r²
Total surface area of a closed cylinder is:
A = L + T + B = 2 π r h + 2(π r²) = 2 π r (h+r)
Volume of a cylinder:
V = π r² h
Given the radius r and lateral surface area L of a cylinder calculate the height h, top and bottom surface area T and B , total surface area A and volume V (Given r, L calculate h, T, B, A, V)
Height of a cylinder
h = L/(2 π r)
Top and bottom surface area of a cylinder (2 circles):
T = B = π r²
Total surface area of a closed cylinder is:
A = L + T + B = 2 π r² + L
Volume of a cylinder:
V = π r² h = π r² L/(2 π r) = r L / 2
Given height h and lateral surface area L calculate the radius r, top and bottom surface area T and B , total surface area A and volume V (Given h, L calculate r, T, B, A, V)
Radius of a cylinder
r = L/(2 π h)
Top and bottom surface area of a cylinder (2 circles):
T = B = π r² = π (L/(2 π h))² = (π L²) / (4 π h²)
Total surface area of a closed cylinder is:
A = L + T + B = L + (π L²) / (2 π h²)
Volume of a cylinder:
V = π (L/(2 π h))² h = π L² / (4 h)
Given the radius r and volume V of a cylinder calculate the height h, lateral surface area L, top and bottom surface area T and B , total surface area A and(Given r, V calculate h, L, T, B, A)
Height of a cylinder
h = V/(π r²)
Lateral surface area of a cylinder (just the curved outside):
L = 2 π r h = 2 π r V/(π r²) = 2 V / r
Top and bottom surface area of a cylinder (2 circles):
T = B = π r²
Total surface area of a closed cylinder is:
A = L + T + B = 2 V / r + 2 π r²
Given the height h and volume V of a cylinder calculate the radius r, lateral surface area L, top and bottom surface area T and B , total surface area A(Given h, V calculate h, L, T, B, A)
Radius of a cylinder
r = √(V / (πh))
Lateral surface area of a cylinder (just the curved outside):
L = 2 π r h = 2 π √(V / (πh)) h = 2 √(π V h)
Top and bottom surface area of a cylinder (2 circles):
T = B = π r² = π (√(V / (πh)))² = V/h
Total surface area of a closed cylinder is:
A = L + T + B = 2 √(π V h) + 2V/h
What are the Properties of a Cylinder Shape?
The bases are always congruent and parallel.
If the axis forms a right angle with the bases, which are exactly over each other, then it is called a “Right Cylinder”.
It is similar to the prism since it has the same cross-section everywhere.
If the bases are not exactly over each other but sideways, and the axis does not produce the right angle to the bases, then it is called “Oblique Cylinder”.
If the bases are circular in shape, then it is called a right circular cylinder.
If the bases are in an elliptical shape, then it is called an “Elliptical Cylinder”.
