A cylinder has a radius of 6 inches and a height of h inches. If a cub

Question

A cylinder has a radius of 6 inches and a height of h inches. If a cube of the same surface area has a height of h√π, what is the value of h?

A. 3
B. 6
C. 1 − √13
D. 1 + √13
E. 1 + √26

MarmikUpadhyay · Answer

From data:
Total surface area of cylinder =  2πr * (h + r) = 12π * (h + 6) 
Surface area of cube =  6 * a^2 = 6 * (h√π)^2 = 6πh^2

Both have the same surface area.
=>  12π * (h + 6) = 6πh^2 
=>  2h + 12 = h^2 
=>  h^2 - 2h - 12 = 0 
=> h = 1 + √13 or 1 - √13

h cannot be negative.

So, correct answer is option  D .

stne · Answer

How did you go from  h^2 - 2h - 12 = 0  to h = 1 + √13 or 1 - √13

MarmikUpadhyay · Answer

Simply by using the quadratic formula:

h = \frac{-b +- \sqrt{b^2 - 4ac}}{2a}

Fdambro294 · Answer

If R = 6

Surface area of Cylinder = (2) (pi) (6)^2 + (2) (pi) (6) (h)

Surface area of Cube = (6) (edge)^2 = (6) (h * sqrt(pi))^2

72(pi) + (12) (pi) (h) = (6) (h)^2 (pi)

——cancel (pi) in each term on both sides of equation and collect terms on one side——

(6)(h)^2 - (12)(h) - 72 = 0

—-divide by 6 ——

(h)^2 - 2(h) - 12 = 0

(h)^2 - 2(h) + 1 - 12 - 1 = 0

(h -1)^2 = 13

—-because we are dealing with positive lengths take the positive root when taking the square root of both sides

h - 1 = sqrt(3)

1 + sqrt(3)

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