If The Ratio Of Radius Of Cylinder Is 3:5 And Height Of Cylinder Is 2:7 Then Find The Ratio Of Curved Surface Area And Total Surface Area Of Cylinder
**If the Ratio of Radius of Cylinder is 3:5 and Height of Cylinder is 2:7, Then Find the Ratio of Curved Surface Area and Total Surface Area of Cylinder**
Understanding the Basics of Cylinder Surface Area
A cylinder is a three-dimensional shape with two parallel and circular bases connected by a curved lateral surface. The surface area of a cylinder is the total area of its two bases and the curved surface area. The formula to calculate the surface area of a cylinder is:
- Curved Surface Area (CSA) = 2πrh
- Total Surface Area (TSA) = 2πr(h + r)
where r is the radius of the cylinder and h is its height.
Calculating the Ratio of Curved Surface Area and Total Surface Area
Given that the ratio of the radius of the cylinder is 3:5 and the height of the cylinder is 2:7, we can represent the radius and height as 3x and 2y, respectively.
Calculating the Curved Surface Area
The curved surface area of the cylinder is given by the formula CSA = 2πrh. Substituting the values of r and h, we get:
CSA = 2π(3x)(2y) CSA = 12πxy
Calculating the Total Surface Area
The total surface area of the cylinder is given by the formula TSA = 2πr(h + r). Substituting the values of r and h, we get:
TSA = 2π(3x)(2y + 3x) TSA = 6π(2y + 3x)
Finding the Ratio of Curved Surface Area and Total Surface Area
To find the ratio of the curved surface area and the total surface area, we divide the curved surface area by the total surface area:
Ratio = CSA / TSA Ratio = (12πxy) / (6π(2y + 3x)) Ratio = 2xy / (2y + 3x)
Simplifying the Ratio
We can simplify the ratio by dividing both the numerator and the denominator by 2y:
Ratio = x / (y + 1.5x)
Conclusion
In conclusion, the ratio of the curved surface area and the total surface area of a cylinder with a radius ratio of 3:5 and a height ratio of 2:7 is x / (y + 1.5x).
Frequently Asked Questions (FAQs)
Q: What is the formula for the curved surface area of a cylinder?
A: The formula for the curved surface area of a cylinder is CSA = 2πrh.
Q: What is the formula for the total surface area of a cylinder?
A: The formula for the total surface area of a cylinder is TSA = 2πr(h + r).
Q: How do I find the ratio of the curved surface area and the total surface area of a cylinder?
A: To find the ratio of the curved surface area and the total surface area of a cylinder, you need to divide the curved surface area by the total surface area.
Q: What is the ratio of the curved surface area and the total surface area of a cylinder with a radius ratio of 3:5 and a height ratio of 2:7?
A: The ratio of the curved surface area and the total surface area of a cylinder with a radius ratio of 3:5 and a height ratio of 2:7 is x / (y + 1.5x).
Q: How do I simplify the ratio of the curved surface area and the total surface area of a cylinder?
A: You can simplify the ratio of the curved surface area and the total surface area of a cylinder by dividing both the numerator and the denominator by 2y.
Q: What is the significance of the ratio of the curved surface area and the total surface area of a cylinder?
A: The ratio of the curved surface area and the total surface area of a cylinder is important in various mathematical and real-world applications, such as calculating the surface area of a cylinder and understanding the relationship between the curved surface area and the total surface area.