The curve surface area of Right circular cylinder of height 40cm is 88 cm Square find the diameter of the base of the cylinder?

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The curve surface area of Right circular cylinder of height 40cm is 88 cm Square find the diameter of the base of the cylinder?

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The curve surface area of Right circular cylinder of height 40cm is 88...

The surface area of a right circular cylinder is given by the formula:

Surface area = 2πr^2 + 2πrh

Where r is the radius of the base of the cylinder, h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14.

If the surface area of a right circular cylinder is 88 cm^2 and the height is 40 cm, we can substitute these values into the formula to solve for the radius:

88 cm^2 = 2πr^2 + 2πrh

88 cm^2 = 2πr^2 + 2πr(40 cm)

88 cm^2 = 2πr^2 + 80πr

88 cm^2 - 80πr = 2πr^2

(88 cm^2 - 80πr)/2π = r^2

44 cm^2 - 40πr/2π = r^2

r^2 = 44 cm^2 - 40πr/2π

r^2 = 22 cm^2 - 20πr/π

r^2 = 22 cm^2 - 20r

r^2 + 20r - 22 cm^2 = 0

We can use the quadratic formula to solve for r:

r = (-20 +- √(400 + 880))/2

r = (-20 +- √1280)/2

r = (-20 +- 35.6)/2

The radius of the base of the cylinder is either 7.8 cm or -12.8 cm. However, the radius cannot be negative, so the radius must be 7.8 cm.

The diameter of the base of the cylinder is twice the radius, or 2 * 7.8 cm = 15.6 cm. Therefore, the diameter of the base of the cylinder is 15.6 cm.

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