Quick and easy learning is possible by understanding the concept of cylinders in depth. We will help you out to find the problems on the right circular cylinder. Step by step explanation for different types of questions related to the right circular cylinder is available on this page. In addition to this, you can also know how to relate the formulas for all solid figures here. Hence make use of this page and practice the problems without any delay.
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Right Circular Cylinder Examples with Solutions
Check out the problems given below to know how to find the surface area and volume of the right circular cylinder.
Example 1.
Find the volume of a right cylinder, if the radius and height of the cylinder are 10 cm and 20 cm respectively.
Solution:
Given that
Radius = r = 10 cm
Height = h = 20 cm
We know that
Volume of a right cylinder = πr²h cubic units
Therefore, using the formula, we get
Volume of a right cylinder = 3.14 × 10² × 20
= 3.14 × 10 × 10 × 20
= 6280
Hence, the volume of the given right cylinder is 6280 cm³.
Example 2.
The radius and height of a right cylinder are given as 4 m and 6.5 m respectively. Find the volume and total surface area of the right cylinder.
Solution:
Given that
radius = r = 4 m
Height = h = 6.5 m
We know that
Volume of a right cylinder = πr²h cubic units
Therefore,
Volume of a right cylinder = 3.14 × 4² × 6.5
= 3.14 × 16 × 6.5
= 326.56
Hence, the volume of the given right cylinder is 326.56 cubic m.
The total surface area of the right cylinder = Area of circular base + Curved Surface Area
Total surface area of a right cylinder = 2πr(h + r) square units
Putting the values of radius and height in the above formula
Total surface area = 2 x π x 4(6.5 + 4)
Total surface area= 2 x 3.14 x 4 x 10.5
Total surface area= 263.76 sq.m
Hence, the total surface area of the given right cylinder is 263.76 m².
Example 3.
What is the curved surface area of the right circular cylinder having a radius of 10 units and a height of 11 units?
Solution:
Given that
Radius = r = 10 units,
Height = h = 11 units and the curved surface area of a right circular cylinder = 2πrh
Curved surface area of a right circular cylinder = 2 × (22/7) × 10 × 11
= 276.32square units.
Therefore the curved surface area of the right circular cylinder is 276.32 square units
Example 4.
The curved surface area of a right circular cylinder of height is 132 cm². The height of the cylinder is 7cm. Find the radius and of the base of the cylinder.
Solution:
Let r be the radius and h be the height of the cylinder.
The curved surface area of right circular cylinder = 2πrh = 132
h = 7cm
2πrh = 88
2 x 22/7 x r x 7 = 132
44r = 132
r = 132/44
r = 3cm
Diameter = 2r
= 2 × 3
= 6cm
So the radius and diameter of the right circular cylinder are 3cm and 6cm
Example 5.
The radius of a cylindrical water bottle is 3cm, and whose height is 6cm. Find the capacity of water in the bottle?
Solution:
Given that
The radius of the bottle = r = 3cm The height of the bottle = h= 6cm.
We know that the capacity of the bottle is known as the volume of the cylinder.
The volume of the cylinder with radius ‘r′ and height ‘h′ is πr²h.
= 22/7×3²×6
= 22/7 × 9 × 6
= 169.56
= 62.86 cm³
Hence, the capacity of the water bottle is = 169.86 cm³
Example 6.
The volume of the cylinder is 20m³. And, the height of the cylinder is 10m, then find the base radius of the cylinder?
Solution:
Given that
Let the base radius of the cylinder is r meters.
Given that
The volume of the cylinder = 20m³
Height of the cylinder (h)=10m.
We know that the volume of the cylinder with radius ‘r′ and height ‘h′ is πr²h.
20=22/7×(r)²×10
20=22/7×(r)²
r²= 6.36
r= 2.52
Hence, the base radius of the cylinder is 2.52 m.
Example 7.
The radii of two right circular cylinders are in the ratio 3 : 4 and their heights are in the ratio 6 : 5. Find the ratio between their curved surface areas.
Solution:
Given that
If the radii of two cylinders be r1 and r2
let r1 = 3x
r2 = 4x.
Similarly, if the heights of two cylinders are h1 and h2,
let h1 = 6y
h2 = 5y.
Ratio between their curved surface area = 2πr1h1/2πr2h2
= 2π×3x×6y/2π×4x×5y
=9/10
= 9 : 10
Example 8.
Base area of a right circular cylinder is 40cm². If its height is 3 cm, then the volume is equal to.
Solution:
Given that
Height = h = 3 cm
Base area = 40 cm²
We know that base area = πr²
πr² = 40
r² = 40/π
= 12.7
r = 3.56 cm
We know that
The volume of the cylinder = πr²h
= 22/7 ×(3.56)² × 3
= 119.38 cm³
Example 9.
The curved surface area of a right circular cylinder of height is 200 cm². The height of the cylinder is 5cm. Find the radius and of the base of the cylinder.
Solution:
Let r be the radius and h be the height of the cylinder.
The curved surface area of right circular cylinder = 2πrh = 200
h = 5 cm
2πrh = 200
2 x 22/7 x r x 5 = 200
31.4r = 200
r = 200/31.4
r = 63.69 cm
Diameter = 2r
= 2 × 63.69
= 127.38 cm
So the radius and diameter of the right circular cylinder are 63.69 cm and 127.38 cm
Example 10.
Find the volume of a right cylinder, if the radius and height of the cylinder are 18 cm and 26 cm respectively.
Solution:
Given that
Radius = r = 18 cm
Height = h = 26 cm
We know that
Volume of a right cylinder = πr²h cubic units
Therefore, using the formula, we get
Volume of a right cylinder = 3.14 × 18² × 26
= 3.14 × 18 × 18 × 26
= 26451
Hence, the volume of the given right cylinder is 26451 cm³.