Question

Guyss please help me with this question. I tried a thousand times but it's still incorrect.

Answer 1

Answer: $17.68cm$

Step-by-step explanation:

Using the area formula of a cone, find the height first.

$A=\pi r(r+\sqrt{h^2+r^2})$

Solve for h,

Begin by dividing by $\pi r$

$\frac{A}{\pi r}=r+\sqrt{h^2+r^2}$

Subtract r.

$\frac{A}{\pi r}-r=\sqrt{h^2+r^2}$

Square both sides.

$(\frac{A}{\pi r}-r)^2=(\sqrt{h^2+r^2})^2$

$(\frac{A}{\pi r}-r)^2=h^2+r^2$

Subtract $r^2$

$(\frac{A}{\pi r}-r)^2-r^2=h^2$

Extract the square root.

$\sqrt{(\frac{A}{\pi r}-r)^2-r^2 } =\sqrt{h^2}$

$\sqrt{(\frac{A}{\pi r}-r)^2-r^2 } =h$

Plug in your values.

$\sqrt{[\frac{670cm^2}{(3.14)(8cm)}-(8cm)]^2-(8cm)^2 } =h$

Solve;

$\sqrt{[\frac{670cm^2}{25.12cm}-(8cm)]^2-(8cm)^2 } =h$

$\sqrt{[26.67cm-(8cm)]^2-(8cm)^2 } =h$

$\sqrt{(18.67cm)^2-(8cm)^2 } =h$

$\sqrt{348.57cm^2-64cm^2}=h$

$\sqrt{284.57cm^2}=h$

$15.77cm=h$

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Now, to find the slant height use this formula: $l=\sqrt{h^2+r^2}$

$l=\sqrt{(15.77cm)^2+(8cm)^2}\\l=\sqrt{248.69cm^2+64cm^2}\\ l=\sqrt{312.69cm^2}\\ l=17.68cm$