The curved surface area of a cylinder is 2π (y² - 7y + 12) and its radius is (y - 3). Find the height of the cylinder (C.S.A. of cylinder = 2πrh).

Solution:

Given curved surface area of the cylinder = 2π (y² - 7y + 12) and radius = (y - 3)

Curved surface area of cylinder = 2πrh

∴ h = 2π (y² - 7y + 12) / 2π (y - 3)

h = [(y² - 4y - 3y + 12)] / (y - 3)

h = [y(y - 4) - 3(y - 4)] / (y - 3)

h = [(y - 4) (y - 3)] / (y - 3)

h = (y - 4)

✦ Try This: The curved surface area of a cylinder is 2π (x² + 9x + 20) and its radius is (x + 5). Find the height of the cylinder.

Given curved surface area of the cylinder = 2π (x² + 9x + 20) and radius = (x + 5)

Curved surface area of cylinder = 2πrh

∴ h = 2π (x² + 9x + 20) / 2π (x+5)

h = [(x² + 4x + 5x + 20)] / (x+5)

h = [x(x + 4) + 5(x + 4)] / (x+5)

h = [(x + 5) (x + 4)] / (x+5)

h = (x + 4)

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Problem 100

Summary:

The curved surface area of a cylinder is 2π (y² - 7y + 12) and its radius is (y - 3). The height of the cylinderis (y - 4)

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