# Oblique Cylinder

An oblique cylinder is a type of cylinder where the 2 bases are parallel but not directly aligned to each other. It is just a tilted or a slanted cylinder having its sides not perpendicular to the 2 bases.

Thus the sides of an oblique cylinder lean over at an angle that is not 90°. An oblique cylinder is thus exactly opposite to a right cylinder. The diagram given below is that of an oblique cylinder with its height (h) and radius (r) compared to a right circular cylinder.

Let us now learn about the volume of an oblique cylinder, how they are calculated with solved examples.

## Formulas

### Volume

The volume of an oblique cylinder is the space occupied by the cylinder in the three-dimensional plane. It is same as the volume of a right circular cylinder having the same height. Similar to a right cylinder it is measured in cubic units such as m3, cm3, mm3, ft3.

The formula to calculate the volume of an oblique cylinder is given below:

As we know,

Volume (V) = Base area of cylinder × height of cylinder

= (π × r2) × h

= πr2h

Let us solve an example to understand the concept better.

Find the volume of a slanted cylinder whose radius is 11 inches and height is 24 inches. (Use π = 3.141).

Solution:

As we know,
Volume (V) = πr2h, here π = 22/7 = 3.141, r = 11 in, h = 24 in
= 3.141 × 11 × 11 × 24
= 9121.464 in2

### Surface Area

Like a right circular cylinder, an oblique cylinder also has two types of surface areas. They are discussed below with formulas and solved examples.

#### Lateral (Curved) Surface Area

The lateral or the curved surface area (LSA) of a cylinder is the area formed by the curved surface of the cylinder. It is thus the space occupied between the two parallel circular bases. The formula to calculate the LSA of an oblique cylinder is given below:

Let us solve an example to understand the concept better.

Calculate the curved surface area of the oblique cylinder with a radius of 5 cm and a length of 15 cm.

Solution:

As we know,
Curved Surface Area (CSA) = 2πrl, here π = 3.141, r = 5 cm, l = 15 cm
= (2 × 3.141) × 5 × 15
= 471.15 cm2

#### Total Surface Area

The total surface area (TSA) of an oblique cylinder is the area occupied by the entire cylinder. It includes the area of 2 circular bases and 1 curved surface. The formula to calculate the TSA of an oblique cylinder is given below:

Let us solve an example to understand the concept better.

The radius of a slanted cylinder is 11 ft. Find the total surface area of the cylinder with a length of 33 ft.

Solution:

As we know,
Total Surface Area (TSA) = l + 2πr2, here l = 33 ft, π = 3.141, r = 11 ft
= 33 + (2 × 3.141 × 11 × 11)
= 33 + 760.122
= 793.122 ft2