Question

I need some quick help on this one question.

A team of engineers must design a fuel tank in the shape of a cone. The surface area of a cone (excluding the base) is given by the formula

S = pi*sqrt(r^2 + h^2)

Find the radius of a cone with a height of 21 meters and a surface area of 155 meters squared. Round your answer to the nearest tenth if necessary.

Answer 1

@AloneS
@Elsa213

Answer 2

@SeanStewart16

Answer 3

osht dude, was not expecting that XD ill try, but cones beat me up

Answer 4

LOL, sorry, it's the reason I can here, question was beating me up.

Answer 5

Seriously, if you can just help me set up the equation, I could probably get it from there.

Answer 6

You're given everything you need, just a bit of algebra to solve for 'r'

\[\large S = \pi \times \sqrt{r^2 + h^2}\]

Divide both sides by \(\large \pi\)
\[\large \frac{S}{\pi} = \sqrt{r^2 + h^2}\]

Square both sides

\[\large (\frac{S}{\pi})^2 = r^2 + h^2\]

Subtract \(\large h^2\) from both sides

\[\large (\frac{S}{\pi})^2 - h^2 = r^2\]

And take the square root of both sides to solve for 'r'

\[\large r = \sqrt{(\frac{S}{\pi})^2 - h^2}\]

Now just plug in the 'S' they gave you *155* and the 'h' they gave *21* and solve for 'r

Answer 7

Thank you so much man! Life saver!

Answer 8

No problem!