Question

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

Answer 1

Answer:
`17.68cm`

Explanation:

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

`A=\pi r(r+√(h^2+r^2))`

Solve for h,

Begin by dividing by
`\pi r`

`(A)/(\pi r)=r+√(h^2+r^2)`

Subtract r.

`(A)/(\pi r)-r=√(h^2+r^2)`

Square both sides.

`((A)/(\pi r)-r)^2=(√(h^2+r^2))^2`

`((A)/(\pi r)-r)^2=h^2+r^2`

Subtract
`r^2`

`((A)/(\pi r)-r)^2-r^2=h^2`

Extract the square root.

`\sqrt{((A)/(\pi r)-r)^2-r^2 } =√(h^2)`

`\sqrt{((A)/(\pi r)-r)^2-r^2 } =h`

Plug in your values.

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

Solve;

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

`√([26.67cm-(8cm)]^2-(8cm)^2 ) =h`

`√((18.67cm)^2-(8cm)^2 ) =h`

`√(348.57cm^2-64cm^2)=h`

`√(284.57cm^2)=h`

`15.77cm=h`

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Now, to find the slant height use this formula:
`l=√(h^2+r^2)`

`l=√((15.77cm)^2+(8cm)^2)\\l=√(248.69cm^2+64cm^2)\\ l=√(312.69cm^2)\\ l=17.68cm`