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# Oblique Cylinder|Definition & Meaning

## Definition

A cylinder that **“leans over**” or has sides that aren’t parallel to the bases is an oblique cylinder.

Figure 1 illustrates an oblique cylinder. It is a **three-dimensional object** with two straight sides connecting its top and bottom **circular bases**. Oblique cylinders are those whose sides are inclined rather than parallel to their bases. The **top base** is not precisely above the bottom base because of the **cylinder’s slant to one side. **

## Difference Between Right Cylinder and Oblique Cylinder

A cylinder is referred to be a right circular cylinder if the segments **connecting the circular bases’** centers are **perpendicular** to their two planes. An **oblique circular** cylinder is one where the segments connecting the centers of the circles are **not parallel** to the planes of the circles. Figure 2 illustrates the graphical view of the right cylinder and oblique cylinder.

## Volume of an Oblique Cylinder

The area **occupied** **by** an oblique cylinder in a three-dimensional plane is **called** its volume. It is the same as a right cylinder of the same height. Its dimensions are expressed in cubic units like **cubic meters,cubic centimeters****, cubic ****millimeters, and cubic feet**

**,**much like a

**right cylinder. Figure 3**illustrates the graphical view of the volume of an oblique cylinder.

## Curved Surface Area of an Oblique Cylinder

The region created by a **cylinder’s curved surface** is known as the lateral or curved surface area (LSA). Therefore, it is the area that is occupied by the **two parallel circular bases. **The curved surface area of an oblique cylinder is calculated using the formula:

Curved Surface Area (CSA) = 2$\pi$RL

**where** L is the length of one of the **slanted** **sides** and R is the radius of the circle.

## Total Surface Area of an Oblique Cylinder

The area that the full **oblique cylinder** occupies is known as its **total surface area** (TSA). It covers the space occupied by two round bases and one curved surface. The formula for the total Surface area of an oblique cylinder is given below:

Total surface area (TSA) = L + 2$\pi$R^{2}

Again, L is the length of one of the **slanted** **sides,** and R is the radius of the circle.

## Examples of Oblique Cylinder

**Example 1**

a) If the height of the **oblique cylinder** is 24 inches and the diameter of the cylinder is 22 inches. Find the **volume** of an oblique cylinder.

b) The radius of an oblique cylinder is equal to 4 cm, and the length of the cylinder is 10cm. Find the **curved surface area** of the oblique cylinder.

c) Find the volume of an oblique cylinder if the height of the cylinder is 5 cm and the volume of the **cylinder is 25 cubic cm.**

**Solution**

a) As we know, the volume of an oblique cylinder is:

Volume=$\pi$r^{2}h

As we have the diameter of the cylinder so the radius will be equal to $\mathsf{\dfrac{22}{2}} = 11$.

So the volume of the cylinder is equal to:

Volume = (3.412)(11)(11)(24)

**Volume = 9121.464 cubic inches**

b) The formula for the curved surface area is:

Curved Surface Area (CSA) = 2$\pi$rl

Curved Surface Area (CSA) = 2(3.142) (4)(10)

**Curved Surface Area (CSA) = 251.36 sq cm**

c) As we know that:

Volume = $\pi$r^{2}h

The volume of the cylinder is given as 25 cubic cm, while the height of the cylinder is given as 5 cm.

25 = 3.412 $\times$ r^{2} $\times$ 5

$\mathsf{\dfrac{25}{5}}$ = 3.1412 $\times$ r^{2}

$\mathsf{\dfrac{5}{3.141}}$ = r^{2}

r^{2} = 1.59

**r = 1.26 cm**

The radius of the given cylinder is equal to **1.26 cm**.

**Example 2**

a) If the height of the oblique cylinder is 20 inches and the diameter of the cylinder is 10 inches. Find the volume of an oblique cylinder.

b) The radius of an oblique cylinder is equal to 10 cm, and the length of the cylinder is 20cm. Find the curved surface area of the oblique cylinder.

**Solution**

a) As we know, the volume of an oblique cylinder is:

Volume = $\pi$r^{2}h

As we have the diameter of the cylinder so the radius will be equal to $\mathsf{\dfrac{10}{2}} = 5$.

So the volume of the cylinder is equal to:

Volume = (3.412)(5)(5)(20)

**Volume = 1570.6 cubic inches**

b) The formula for the curved surface area is:

Curved Surface Area (CSA) = 2$\pi$rl

Curved Surface Area (CSA) = 2(3.142)(10)(20)

**Curved Surface Area (CSA) = 1256.48 sq cm**

### Example 3

a) Find the volume of an oblique cylinder if the height of the cylinder is 5 cubic cm and the **volume of the cylinder** is 30 cubic cm.

b) Find the total surface area of an oblique cylinder if the radius of the cylinder is equal to 25 cm and the** length of the cylinder** is 15 cm.

### Solution

a) As we know that:

Volume = $\pi$r^{2}h

The volume of the cylinder is given as 30 cubic cm, while the height of the cylinder is given as 5 cm.

30 = 3.1412 $\times$ r^{2} $\times$ 5

$\mathsf{\dfrac{30}{5}}$= 3.1412 $\times$ r^{2}

$\mathsf{\dfrac{6}{3.141}}$ = r^{2}

r^{2} = 1.91

**r = 1.34 cm**

The radius of the given cylinder is equal to **1.34 cm**.

b) As we know, the formula for the total surface area of the cylinder:

TSA = l + 2$\pi$r^{2}

The length of the cylinder is given as 15 cm, and the radius of the cylinder is 25 cm, so:

Total surface area (TSA) = 15 + 2(3.142)(25)(25)

Total surface area (TSA) = 15 + 2(3.142)(625)

Total surface area (TSA) = 15 + 3927.5

**Total surface area (TSA) = 3942.5 sq cm**

So the total surface area of an oblique cylinder, according to the given data, is equal to **3942.5 sq cm**.

### Example 4

Find the length of an oblique cylinder if the radius of the cylinder is equal to 25 cm and the **surface area of the cylinder** is 4200 sq cm.

### Solution

As we know, the formula for the total surface area of the cylinder:

TSA = l + 2$\pi$r^{2}

The length of the cylinder is given as 15 cm, and the radius of the cylinder is 25 cm, so:

Total surface area (TSA) = 15 + 2(3.142)(25)(25)

4200 = l + 2(3.142)(625)

4200 – 3927.5 = l

**Length of an oblique cylinder = 272.5 cm**

So the length of the cylinder is equal to 272.5 cm if the total surface area is equal to **4200 sq cm**.

*All images were created using GeoGebra.*