A cylinder is cut into three parts by two cuts parallel to its base. C

1.	A cylinder is cut into three parts by two cuts parallel to its base. Cuts are made on equal heights. If the radius of that cylinder is 3 times its height, Find the ratio between Increased surface area and original Surface area.1. 5 : 22. 3 : 23. 3 : 44. 4 : 3
Answer» Correct Answer - Option 2 : 3 : 2 Given: Radius of original cylinder is 3 times the height. Two cuts made parallel to base of equal heights. Formula Used: Total Surface Area = 2πr(h + r), where r is radius of base and h is height of cylinder Concept Used: Since Base of a cylinder is circle, so after every cut parallel to base, there will be an increase of two new circles with area πr² each. Calculation: Let the height of original cylinder be 3x then radius will be 9x units Total Surface Area of original Cylinder = (2π × 9x)(3x + 9x) ⇒ T.S.A. = 216πx² Using the Statement of concept used, One cut will produce 2 new circles then 2 cuts will form 4 new circles. Increased Surface Area = 4π × (9x)² ⇒ Increased Surface Area = 324πx² Increased surface area/Original surface area = 324πx²/216πx² ⇒ Increased surface area/Original surface area = 3/2 ∴ The ratio of Increased surface area and original Surface area is 3 : 2

A cylinder is cut into three parts by two cuts parallel to its base. Cuts are made on equal heights. If the radius of that cylinder is 3 times its height, Find the ratio between Increased surface area and original Surface area.1. 5 : 22. 3 : 23. 3 : 44. 4 : 3

Answer» Correct Answer - Option 2 : 3 : 2

Given:

Radius of original cylinder is 3 times the height.

Two cuts made parallel to base of equal heights.

Formula Used:

Total Surface Area = 2πr(h + r), where r is radius of base and h is height of cylinder

Concept Used:

Since Base of a cylinder is circle, so after every cut parallel to base, there will be an increase of two new circles with area πr² each.

Calculation:

Let the height of original cylinder be 3x then radius will be 9x units

Total Surface Area of original Cylinder = (2π × 9x)(3x + 9x)

⇒ T.S.A. = 216πx²

Using the Statement of concept used,

One cut will produce 2 new circles then 2 cuts will form 4 new circles.

Increased Surface Area = 4π × (9x)²

⇒ Increased Surface Area = 324πx²

Increased surface area/Original surface area = 324πx²/216πx²

⇒ Increased surface area/Original surface area = 3/2

∴ The ratio of Increased surface area and original Surface area is 3 : 2