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Area of Hollow Cylinder

A Hollow Cylinder is a Geometric Shape that is empty or hollow from the inside and that is why its internal and external radii are different.

Hollow Cylinder is a three-dimensional Geometric Shape that is hollow from the inside. It is different from a Solid Cylinder in that, the Solid Cylinder is not hollow that is, the Solid Cylinder is made up of some mass or some material. The Solid Cylinder has one Radius as opposed to the two radii of the Hollow Cylinder. Now we will see one figure related to Solid Cylinder and another one related to Hollow Cylinder to help us better understand the difference between Solid Cylinder and Hollow Cylinder.

Solid Cylinder vs Hollow Cylinder-

In this figure, we can easily see the difference between a Solid Cylinder and a Hollow Cylinder. We can briefly describe the difference between The Hollow Cylinder and The Solid Cylinder as, The Solid Cylinder is Solid in shape, meaning, it has no empty space between its boundaries, whereas The Hollow Cylinder has empty space between its boundaries.

We can also see from the above figure that The Solid Cylinder has only one Radius mentioned in the above figure. In the Hollow Cylinder, there are two radii, mentioned as “Internal Radius” and “External Radius”. We will further see the difference between The Hollow Cylinder and The Solid Cylinder when we try to calculate The Area and The Volume of both The Hollow Cylinder and The Solid Cylinder.

Area

In this topic, we will see the Area of both The Hollow Cylinder and The Solid Cylinder.

First, we will see how to calculate the Area of The Hollow Cylinder.

To calculate the Total Surface Area (TSA) of a Hollow Cylinder, we have to calculate the Lateral Surface Area (LSA) first.

So,

Lateral Surface Area is equal to the sum of External Surface Area (ESA) and Internal Surface Area (ISA).

So, to calculate that,

LSA=ESA+ISA

LSA=2*π*R*h+2*π*r*h

LSA=2πRh+2πrh

LSA=2πh(R+r)

This is Lateral Surface Area.

Now, The Total Surface Area (TSA) is the sum of The Lateral Surface Area (LSA) and the Sum of The Areas of The Solid Bases (ASB).

TSA= LSA+ASB

TSA= 2πh(R+r) + 2π (R²r²)

Now we will calculate the Area of the Solid Cylinder and below we will see a figure to help us understand this.

Now we will calculate the Total Surface Area (TSA) of this Solid Cylinder. But first, we have to calculate the Curved Surface Area (CSA).

CSA=2*π*r*h

CSA=2πrh

So the Total Surface Area (TSA),

TSA= 2πrh + πr²+πr²

TSA= 2πrh + 2πr²

TSA= 2πr (h+r)

Volume

Now we will have to calculate the volumes of both The Hollow Cylinder and The Solid Cylinder. In order to do that, we have to see the figures pertaining to both The Hollow Cylinder and The Solid Cylinder.

From the above figure, we can see that the Volume of The Hollow Cylinder is equal to,

V=π (R²-r²)h

Now we will see how to calculate the Volume of a Solid Cylinder with the help of a diagram:-

The volume of the Solid Cylinder like the one given in the above figure is:-

V=πr²h

So now that we have calculated the Area and Volume of both The Hollow Cylinder and The Solid Cylinder, we can now move to some solved problems that will use the topics that we have just learned.

Solved Problems

Find the volume of a Hollow Cylinder whose outer radius is 9 and whose internal radius is 7 and whose height is 9. (Use π= (22/7)).

Soln.

As we have learned earlier in this topic, Volume of a Hollow Cylinder,

V=π (R²-r²) h

V= (22/7) *(92-72)*(9)

V= (22/7) *(81-49)*(9)

V= (22/7)*288

V=905.143

Find the volume of a Hollow Cylinder whose Outer Radius is 12 and whose internal radius is 8 and whose height is 7. (Use π= (22/7)).

Soln.

As we have learned earlier in this topic, Volume of a Hollow Cylinder,

V=π (R²-r²) h

So substituting the values given in the question in the above formula,

V= (22/7) *(122-82)*(7)

V= (22/7) *(144-64)*(7)

V=1760

Find the volume of a solid cylinder with radius=5 and height=5. (Use π= (22/7)).

Soln.

As we have learned in the above topics,

V=πr²h

V= (22/7)*(52)*(5)

V= (22/7)*(53)

V=392.857

Find the volume of a solid cylinder with radius=7 and height=6. (Use π=(22/7)).

Soln.

As we have learned in the above topics, the volume of a Solid Cylinder is given by:-

V=πr²h

V= (22/7)*(72)*(6)

V=924

Find the area of a hollow cylinder with an external radius 7, an internal radius of 6, and a height of 5. (Use π= (22/7)).

Soln.

We already know the formula of Area of a Hollow Cylinder,

TSA= 2πh(R+r) + 2π (R²-r²)

TSA= 2× (22/7) × 5× (7+6) + 2× (22/7) × (72-62)

TSA=2× (22/7) × 5 × 13 + 2× (22/7) ×13

TSA= 408.571+81.714

TSA=490.285

Find the area of a hollow cylinder with an external radius 9, an internal radius of 6, and a height of 4. (Use π= (22/7)).

Soln.

We already know the formula of Area of a Hollow Cylinder,

TSA= 2πh(R+r) + 2π (R²-r²)

TSA= 2× (22/7) ×4× (9+6) + 2× (22/7) × (92-62)

TSA=377.143+282.857

TSA=660

Find the area of a solid cylinder with a radius of 5 and height of 3. (Use π= (22/7)).

Soln.

Area of a solid cylinder,

TSA= 2πr (h+r)

TSA= 2× (22/7) ×5× (3+5)

TSA= 251.428

Find the area of a solid cylinder with a radius of 6 and height of 4. (Use π= (22/7)).

Soln.

Area of a solid cylinder,

TSA= 2πr (h+r)

TSA= 2× (22/7) × 6 × (4+6)

TSA= 377.143

Conclusion

In this article, we described The Hollow Cylinder in brief. Then we compared the Hollow Cylinder with the Solid Cylinder. We discussed how to calculate the hollow cylinder and The Solid Cylinder. We talked about how to calculate the volume of both of these geometric figures. Finally, we solved some problems related to these topics.