Cylinder Calculation - Calculation of Volume, Lateral Surface Area, Total Surface Area, Circumference of the Base and Diameter

The cylinder radius r, also known as the radius, is the distance between the cylinder's axis (i.e., the centre of the cylinder's base surface) and the curved surface.

The cylinder diameter d or ⌀ is the length of the connecting distance between two points on the circular line through the centre M of the cylinder base.

The circumference of the base C of a cylinder is the distance around the circular edge of the base of the cylinder.

The base area B is the area enclosed by the cylinder surface. The base area of the cylinder is actually the area of a circle, since the base of the cylinder is a circle.

B = r² × π

The height h of a cylinder corresponds to the distance between the two parallel cylinder bases.

The cylinder volume V describes the spatial expansion of a cylinder.

V = B × h

The development of the cylinder surface area LSA (Curved Surface Area or Lateral Surface Area) is a rectangle whose length and width correspond to the height h of the cylinder and the circumference of the base C of the cylinder.

LSA = h × C

The total surface area TSA of a cylinder is made up of twice the base area B and the lateral surface area LSA of the cylinder.

TSA = 2 × B + LSA

Given a cylinder with a diameter d of 5 in. We are looking for the radius r of the cylinder.

Calculation

The cylinder radius r corresponds to half the diameter d, i.e., r = d / 2.

If the 5 in chosen in the example are used for the diameter d, the radius of the cylinder is r =  5 in / 2 = 2.5 in.

Given a cylinder with a circumference of the base C of 15 in. We are looking for the radius r of the cylinder.

Calculation

The formula for the cylinder circumference of the base C is C = 2 × r × π. If we convert this formula to r, the radius r is equal to half the division of the circumference of the base divided by pi (π = 3.1415...), i.e., r = C / π / 2.

If we substitute the 15 in chosen in the example for the circumference of the base C, the radius of the cylinder is r = 15 in / π / 2 ≈ 2.39 in.

Let a cylinder with a base area B of 20 in² be given. We are looking for the radius r of the cylinder.

Calculation

The general formula for the base area B is B = r² × π. If we convert this formula to r, the radius r corresponds to the square root of the result of the base area B divided by Pi (π = 3.1415...), i.e., r = B / π.

If the 20 in² chosen in the example are used for the base area B, the radius of the cylinder is r = 20 in² / π ≈ 2.52 in.

Let a cylinder with a radius r of 2.5 in be given. We are looking for the diameter d of the cylinder.

Calculation

The diameter d corresponds to twice the radius r, i.e., d = 2 × r.

If the 2.5 in chosen in the example is used for the radius r, the diameter of the cylinder is d = 2 × 2.5 in = 5 in.

Given is a cylinder with a circumference of the base C of 15 in. We are looking for the diameter d of the cylinder.

Calculation

The formula for the circumference of the base is C = d × π. If we convert this formula to d, the diameter d corresponds to the division of circumference of the base divided by pi (π = 3.1415...), thus d = C / π.

If the 15 in chosen in the example are used for the circumference of the base C, the diameter of the cylinder is d = 15 in / π ≈ 4.77 in.

Let a cylinder with a base area B of 20 in² be given. We are looking for the diameter d of the cylinder.

Calculation

The general formula for the base area B is B = r² × π. Since the diameter d corresponds to twice the radius r, the following formula applies: B = (d / 2)² × π. If we convert this formula to d, the diameter d is equal to twice the square root of the division of the base area B divided by Pi (π = 3.1415...), i.e., d = 2 × B / π.

Substituting the 20 in² chosen in the example for the base area B, the diameter of the cylinder is d = 2 × 20 in / π ≈ 5.05 in.

Given a cylinder with a radius r of 2.5 in. We are looking for the cylinder circumference of the base C of the cylinder.

Calculation

The circumference of the base C corresponds to twice the radius r multiplied by the number Pi (π = 3.1415...), thus C = 2 × r × π.

If the 2.5 in chosen for the radius r in the example are used, the circumference of the base of the cylinder is C = 2 × 2.5 in × π ≈ 15.71 in.

Given a cylinder with a diameter d of 5 in. We are looking for the circumference of the base C of the cylinder.

Calculation

The circumference of the base C corresponds to the diameter d multiplied by the number Pi (π = 3.1415...), thus C = d × π.

Substituting the 5 in chosen in the example for the diameter d, the circumference of the base of the cylinder is C = 5 in × π ≈ 15.71 in.

Let a cylinder with a base area B of 20 in² be given. We are looking for the circumference of the base C of the cylinder.

Calculation

The general formula for the base area B is B = r² × π.

Intermediate calculation radius

Using this formula, the radius r can now be calculated by converting the formula to r. The radius r then corresponds to the root of the result of the base area B divided by Pi (π = 3.1415...), i.e., r = G / π.

If we substitute the 20 in² chosen in the example for the base area B, the radius of the cylinder is r = 20 in / π ≈ 2.52 in.

Calculating the perimeter of the base

Using the radius calculated in this way, the general formula for calculating the circumference of the base can now be used: The circumference of the base C of the cylinder corresponds to twice the radius r multiplied by the number Pi (π = 3.1415...), i.e., C = 2 × r × π.

If we insert the previously calculated value for the radius r, the circumference of the base of the cylinder is C = 2 × 2.52 in × π ≈ 15.85 in.

Let a cylinder with a radius r of 2.5 in be given. We are looking for the base area B of the cylinder.

Calculation

The base area B is equal to the square of the radius, i.e., r² multiplied by the number Pi (π = 3.1415...), and thus B = r² × π.

If we substitute the 2.5 in chosen in the example for the radius r, the base area of the cylinder is B = (2.5 in)² × π ≈ 19.63 in².

Given a cylinder with a diameter d of 5 in. We are looking for the base area B of the cylinder.

Calculation

The base area B is equal to half the diameter squared, i.e., (d / 2)² multiplied by the number Pi (π = 3.1415...), and thus B = (d / 2)² × π.

If we insert the 5 in chosen in the example for the diameter d, the base area B of the cylinder is B = (5 in / 2)² × π ≈ 19.63 in².

Let a cylinder with a circumference of the base C of 15 in be given. We are looking for the base area B of the cylinder.

Calculation

The base area B is derived from the circumference, for example, by first determining the cylinder radius r based on the circumference of the base, because then you can use the common formula for the base area, namely B = r² × π.

Intermediate calculation of radius

So to calculate the radius first, you can rearrange the formula for the cylinder circumference of the base C = 2 × r × π to r, so that you get r = C / π / 2.

Substituting the 15 in chosen in the example for the circumference of the base C, the radius of the cylinder is r = 15 in / π / 2 ≈ 2.39 in.

Calculation of the base area

Finally, if we insert the value calculated here for the radius r, namely 2.39, into the general formula for the base area B = r² × π mentioned earlier, the base area of the cylinder is B = (2.39 in)² × π ≈ 17.90 in².

Let a cylinder with a base area of 20 in² and a volume of 300 in³ be given. We are looking for the height h of the cylinder.

Calculation

The general formula for the volume V of a cylinder is V = B × h, where B is the base area and h is the height of the cylinder. If you convert this formula to h, you get h = V / B. The height h of a cylinder is therefore equal to the cylinder volume V divided by its base area B.

If the values chosen in the example for the volume V and the base area B are used, the height h is h = 300 in³ / 20 in² = 15 in.

Given a cylinder with a base area of 20 in² and a lateral surface area of 200 in². We are looking for the height h of the cylinder.

Calculation

The rolled-up lateral surface (or curved surface) of a cylinder is a rectangle with the height of the cylinder and a width equal to the circumference of the cylinder. If you divide the given lateral surface area LSA by the cylinder circumference of the base C, you get its height. The formula for this is therefore h =  LSA / C.

Intermediate calculation of circumference of the base

The circumference of the base C is obtained from the given base area because, first, B = r² × π applies. Using this formula, the radius r can now be first calculated by converting the formula to r. The radius r then corresponds to the root of the result of the base area B divided by Pi (π = 3.1415...). The radius r then corresponds to the root of the result of the base area B divided by Pi (π = 3.1415...), i.e., r = B / π.

If the value entered for the cylinder base area B is used, the radius of the cylinder is r = 20 in² / π ≈ 2.52 in.

With the radius calculated in this way, the general calculation formula for the cylinder circumference of the base can now be used: The circumference of the base C corresponds to twice the radius r multiplied by the number Pi (π = 3.1415...), thus C =  2 × r × π.

If we insert the previously calculated value for the radius r, the circumference of the base area and thus of the cylinder is C = 2 × 2.52 in × π ≈ 15.85 in.

Calculation of the height

Finally, the value entered for the lateral surface area LSA and the calculated circumference of the base C are substituted into the formula for the height mentioned earlier. Using h =  LSA / C the cylinder height is therefore h = 200 in² / 15.85 in ≈ 12.62 in.

Given a cylinder with a base area of 20 in² and a height of 15 in. We are looking for the volume V of the cylinder.

Calculation

The general formula for the volume V of a cylinder is V = B × h, where B is the base area and h is the height of the cylinder.

IIf we insert the values chosen in the example for the base area B and the height h, the volume V is therefore V = 20 in² × 15 in = 300 in³.

Given a cylinder with a base area of 20 in² and a lateral surface area of 250 in². We are looking for the height h of the cylinder.

Calculation

The general formula for the volume V of a cylinder is V = B × h, where B is the base area and h is the height of the cylinder. The base area B is given in the example. The height h of the cylinder can now be calculated using the given surface area:

The rolled-up lateral surface of a cylinder is a rectangle with the height of the cylinder and a width equal to the circumference of the cylinder base. If you divide the given lateral surface area LSA by the cylinder circumference of the base C, you get its height. The formula for this is therefore h =  LSA / B.

Intermediate calculation of the circumference

The circumference of the base C is obtained from the given base area, because B = r² × π applies first. With the help of this formula, the radius r can now first be calculated by converting the formula to r. The radius r then corresponds to the root of the result of the base area B divided by Pi (π = 3.1415...), i.e., r = B / π.

Substituting the entered value for the cylinder base area B, the radius of the cylinder is r = 20 in² / π ≈ 2.52 in.

With the radius calculated in this way, the general calculation formula for the cylinder circumference of the base can now be used: The circumference of the base C is equal to twice the radius r multiplied by the number Pi (π = 3.1415...), thus C = 2 × r × π.

If we insert the previously calculated value for the radius r, the circumference of the base area and thus of the cylinder is C = 2 × 2.52 in × π ≈ 15.85 in.

Intermediate calculation of height

Finally, using the value entered for the lateral surface area LSA and the circumference of the base calculated above, the cylinder height h is therefore h = 250 in² / 15.85 in ≈ 15.77 in.

Calculation of the volume

The volume V of a cylinder, as mentioned earlier, finally corresponds to the product of the base area B and the height h of the cylinder, i.e., V = B × h.

Finally, if the values for the entered base area B and the height h just calculated from the given surface area are inserted here, the volume is therefore V = 20 in² × 15.77 in ≈ 315.39 in³.

Given a cylinder with a base area of 20 in² and a height of 15 in. We are looking for the lateral surface area (LSA) of the cylinder.

Calculation

The rolled-up lateral surface area LSA of a cylinder is a rectangle with the height h of the cylinder and a width equal to the circumference of the base C of the cylinder. Therefore, the formula LSA = h × C applies.

Intermediate calculation of circumference of the base

The circumference of the base C is obtained on the basis of the given base area, because the following first applies: B = r² × π. Using this formula, the radius r can now be first calculated by converting the formula to r. The radius r then corresponds to the root of the result of the base area B divided by Pi (π = 3.1415...), i.e., r = B / π.

If we insert the entered value for the cylinder base area B, the radius of the cylinder is r = 20 in² / π ≈ 2.52 in.

With the radius calculated in this way, the general formula for calculating the circumference of the cylinder base can now be used: The circumference of the base C corresponds to twice the radius r multiplied by the number Pi (π = 3.1415...), thus C =  2 × r × π.

Substituting the previously calculated value for the radius r, the circumference of the base area and thus of the cylinder is C = 2 × 2.52 in × π ≈ 15.85 in.

Calculation of lateral surface area

If the values entered for the height h and the circumference of the base C calculated in this way are substituted, the lateral surface area LSA is finally LSA = 15 in × 15.85 in ≈ 237.80 in².

Given a cylinder with a base area of 20 in² and a volume of 300 in³. We are looking for the lateral surface area LSA of the cylinder.

Calculation

The rolled-up lateral surface area LSA of a cylinder is a rectangle with the height h of the cylinder and a width equal to the circumference of the base C of the cylinder. The lateral surface area LSA can be calculated using the formula LSA = h × C.

Intermediate calculation of the circumference of the base

The circumference of the base C is obtained from the given base area because, first, B = r² × π applies. Using this formula, the radius r can now be calculated first by rearranging the formula according to r. The radius r then corresponds to the root of the result of the base area B divided by Pi (π = 3.1415...), i.e., r = B / π.

Substituting the entered value for the cylinder base area B, the radius of the cylinder is r = 20 in² / π ≈ 2.52 in.

With the radius calculated in this way, the general formula for calculating the circumference of the cylinder base can now be used: The circumference of the base C corresponds to twice the radius r multiplied by the number Pi (π = 3.1415...), thus C = 2 × r × π.

Substituting the previously calculated value for the radius r, the circumference of the base area and thus of the cylinder is C = 2 × 2.52 in × π ≈ 15.85 in.

Intermediate calculation of height

The height h can be calculated for the given volume V and the given base area B using the following formula: h = V / B.

If we insert the given volume V and the base area B, the height is thus h = 300 in³ / 20 in² = 15 in.

Calculation of the lateral surface area

With the height h calculated in this way and the circumference of the base C of the cylinder already determined, the lateral surface area LSA can now be calculated using the formula LSA = h × C be calculated.

If we insert the calculated values for the height h and the circumference of the base C, the lateral surface area is LSA = 15 in × 15.85 in ≈ 237.80 in².

Given a cylinder with a base area of 20 in² and a lateral surface area of 200 in². We are looking for the total surface area (TSA) of the cylinder.

Calculation

The total surface area TSA is made up of twice the base area B and the lateral surface area LSA, i.e., LSA = 2 × B + CSA.

If we use the 20 in² chosen in the example for the base area B and 200 in² for the lateral surface area LSA, the total surface area TSA of the cylinder is therefore TSA = 2 × 20 in² + 200 in² = 240 in².