Jack knows the surface area of a cylinder and its radius. He wants to find the cylinder's height. He needs to rewrite the formula a=2pi r(r+h) to find the cylinder's height (h) in terms of the cylinder’s surface area (A) and its radius (r). Which is the correct formula?
A h=r+a/2pir
B h=a/2pir
C a/2pir -r^2
D a/2pir -r

Question

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Respuesta :

wolf1728 wolf1728 · Answer 1 · 2017-06-22T19:50:27+02:00

Look at the attached formula (the one on the right).

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boffeemadrid boffeemadrid · Answer 2 · 2019-05-29T07:25:54+02:00

Answer:

(D)[tex]\frac{a}{2{\pi}r}-r=h[/tex]

Step-by-step explanation:

It is given that Jack considers the formula for the surface area of the cylinder and its radius, the formula is:

[tex]a=2{\pi}r(r+h)[/tex] where h is the height of the cylinder and r is the radius of the cylinder.

Upon solving the formula, we have

[tex]a=2{\pi}r(r+h)[/tex]

[tex]a=2{\pi}r^2+2{\pi}rh[/tex]

[tex]a-2{\pi}r^2=2{\pi}rh[/tex]

[tex]\frac{a-2{\pi}r^2}{2{\pi}r}=h[/tex]

[tex]\frac{a}{2{\pi}r}-r=h[/tex]

which is the required correct formula for the height of the cylinder.

Hence, option D is correct.