Area Of Base Cylinder Formula

Surface surface area of a cylinder is defined as the amount of infinite covered by the flat surface of the cylinder's bases and the curved surface of the cylinder. The overall surface area of the cylinder includes the area of the cylinder'due south ii round bases as well as the surface area of the curving surface. For a detailed explanation and derivation of the surface expanse of cylinder formula along with examples read the commodity below

What is Surface Expanse of Cylinder?

A cylinder is a three-dimensional structure formed past two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder. The axis is the line segment that connects the two centers and represents the height of the cylinder. The top view of the cylinder resembles a circumvolve, while the side view resembles a rectangle. A cylinder, dissimilar a cone, cube, or cuboid, lacks vertices due to its curved form and lack of straight lines. It features ii concentric circles on its face.

Surface area of cylinder

Surface Area of Cylinder Formulas

The cylinder'southward surface expanse formula is used to calculate the surface expanse occupied past the cylinder's bases and curving surface. Because a cylinder has a curved surface, nosotros may express both its curved surface area and overall surface area. A cylinder has ii types of surface areas: total surface area and curved surface area. We volition discuss both of them 1 by i.

Curved Surface Surface area of a Cylinder

The curved surface area of the cylinder is enclosed between the two parallel round bases. It is also known every bit the lateral surface expanse. The formula is as follows:

Curved Area = 2πrh

where,

r = radius of the cylinder

h = height of cylinder

Example: Summate the curved surface expanse of the cylinder of radius vii cm and height of 44 cm.

Solution:

We have, r = seven cm and h = 44 cm

Curved surface area of cylinder = 2πrh

= 2 (22/7) (7) (44)

= 2 (22) (five) (two)

= 1936 cm²

Total Surface Area of a Cylinder

A cylinder's total surface area is the sum of its curved surface area and the expanse of its two circular bases. It is calculated by summing the areas of the two bases and the curved surface. As a consequence, the formula for the cylinder's total surface area is equally follows:

Full cylinder surface area = 2πrⁱⁱ + 2πrh = 2πr(r + h)

where,

r = radius of the cylinder

h = peak of cylinder

Example: Calculate the total surface area of the cylinder of radius 7 cm and height of ten cm.

Solution:

Nosotros accept, r = 7 and h = x.

Total surface area = 2πr^two + 2πrh

= 2 (22/7) (vii)² + 2 (22/7) (7) (10)

= 2 (22)(7) + 2 (22) (10)

= 308 + 440

= 748 sq. cm

Derivation of Formula for the Surface Area of Cylinder

Consider a cylinder whose radius is r and meridian is h.

The cylinder is divided into three parts: one circular base, one rectangular area and another round base of operations.

The rectangular area has length of 2πr and breadth of h. So, the area is, A₁ = 2πrh, which is also the curved surface surface area of the cylinder.

The expanse of a round base with radius r is given by, πrⁱⁱ. And so, the surface area of two such bases is, A₂ = (πrⁱⁱ + πr^two) = 2πr^two.

Now, the total area of the cylinder is the sum of above ii areas.

A = A₁ + A₂

= 2πr² + 2πrh

= 2πr(r + h)

This derives the formula for surface surface area of a cylinder.

How to Find the Area of a Cylinder?

Surface area of a cylinder is the area occupied by the bases of cylinder and the area of curved surface of cylinder. Use the steps given below, to find the total surface surface area of a cylinder that has a radius of 14 cm and a height of 10 cm.

Step 1: Mark the radius, 'r', and height, 'h' of cylinder. Think both accept the aforementioned units. Here, given r = fourteen cm, h = 10 cm

Step 2: Here, we take to discover the total area of the cylinder, the formula for the total surface area of the cylinder = 2πr(r + h)

Step three: Put the given values in the above formulas and find the answer in foursquare units. Substitute the values in the formula we go,
Total Area = 2πr(r + h)
= 2π × 14(14 + 10)
= 2π × 336
= two × 3.14 × 336
= 2110.08 foursquare cm

Solved Examples on Surface Surface area of Cylinder

Instance one: Find the curved surface area of the cylinder of radius 3 cm and pinnacle of vii cm.

Solution:

We have, r = 3 and h = 7.

Curved surface area of cylinder = 2πrh

= 2 (22/vii) (3) (7)

= two (22) (3)

= 132 cm²

Example 2: Find the radius of the cylinder of curved surface surface area 220 sq. cm and acme 7 cm.

Solution:

We accept, A = 220 and h = 7.

Curved surface area of cylinder = 2πrh

220 = 2 (22/seven) (r) (7)

220 = 44r

r = 220/44

r = 5 cm

Case 3: Find the full surface area of the cylinder of radius 21 cm and height of 42 cm.

Solution:

Nosotros accept, r = 21 and h = 42.

Total surface surface area = 2πr^two + 2πrh

= 2 (22/seven) (21) (21) + 2 (22/7) (21) (42)

= 2 (22) (three) (21) + ii (22) (3) (42)

= 2772 + 5544

= 8316 sq. cm

Example 4: Find the total surface of the cylinder if curved surface expanse is 176 sq. cm and summit is 21 cm.

Solution:

We have, A = 176 and h = 21.

Curved area of cylinder = 2πrh

176 = 2 (22/7) (r) (21)

176 = two (22) (r) (3)

r = 176/132

r = one.33 cm

Total surface expanse = 2πr² + 2πrh

= 2 (three.14) (ane.33) (1.33) + 176

= xi.10 + 176

= 187.one sq. cm

Example 5: Discover the radius of a cylinder if the sum of its superlative and radius is seven cm such that the total surface surface area is 440 sq. cm.

Solution:

We have, (r + h) = 7 and A = 440.

Total surface surface area = 2πr(r + h)

440 = two (22/7) (r) (7)

2 (22) (r) = 440

44r = 440

r = 10 cm

Case half-dozen: Discover the curved area of a cylinder if its total surface surface area is 528 sq. cm and radius is seven cm.

Solution:

Nosotros have, A = 528 and r = 7 cm.

Total surface area = 2πr(r + h)

528 = ii (22/7) (seven) (7 + h)

2 (22) (7 + h) = 528

vii + h = 12

h = 5 cm

Curved surface area of cylinder = 2πrh

= 2 (22/7) (7) (5)

= ii (22) (five)

= 220 sq. cm

FAQs on Surface area of Cylinder

Question one: What is the cylinder?

Reply:

A cylinder is a three-dimensional shape having 2 circular bases in parallel to each other joined by a curved surface.

Question 2: How to detect the surface surface area of a cylinder?

Respond:

For finding the surface surface area of a cylinder, nosotros will find the surface area of curved surface and surface area of the circular bases of the cylinder. Now add all the areas to get the total surface expanse.

Question 3: Write the formula for finding the area of the cylinder.

Answer:

Formula for finding the surface area of a cylinder is:
Full Surface Surface area = 2πr (h + r) sq. unit
Curved Surface Area = 2πrh sq. unit of measurement
where,
r is the radius and
h is the height of the cylinder

Question 4: Write the formula for the volume of a cylinder.

Answer:

Formula for finding the volume of a cylinder is πr²h cubic units.

Question 5: How to Find the Surface area of an Open up Top Cylinder?

Answer:

Surface area of an open-top cylinder can be calculated by finding the area of bottom circular base and the curved surface of the cylinder and so adding both the result. Thus, the expanse of an open-summit cylinder = πr(r + 2h),
where,
'r' is the radius and
'h' is the tiptop of the cylinder