The radii of two cylinders 3:2 and height 7:4.find the ratios of their curved surface area.
a = 2pi*r*h
a' = 2pi(2/3 r)(4/7 h) = 2pi*rh*8/21
a:a' = 1:8/21 = 21:8
Note that the ratio is just the product of the linear ratios.
Thank you
To find the ratios of the curved surface area of two cylinders, we need to compare their respective curved surface areas.
The curved surface area of a cylinder can be calculated using the formula:
Curved Surface Area = 2 * π * radius * height
Let's assume the radii of the two cylinders are given by ratios 3:2 and the heights are given by ratios 7:4.
1. Start by assigning values to the ratios:
Let the radii of the first cylinder be 3x and the radii of the second cylinder be 2x.
Let the height of the first cylinder be 7y and the height of the second cylinder be 4y.
2. Calculate the curved surface area of the first cylinder:
Curved Surface Area of First Cylinder = 2 * π * (3x) * (7y)
3. Calculate the curved surface area of the second cylinder:
Curved Surface Area of Second Cylinder = 2 * π * (2x) * (4y)
4. Simplify the formulas by multiplying and canceling out common terms:
Curved Surface Area of First Cylinder = 6πxy
Curved Surface Area of Second Cylinder = 16πxy
5. Determine the ratio of the curved surface areas:
Ratio = (Curved Surface Area of First Cylinder) / (Curved Surface Area of Second Cylinder)
= (6πxy) / (16πxy)
= 6/16
= 3/8
Therefore, the ratio of the curved surface areas of the two cylinders is 3:8.