To find the surface area of a cone, we can use the formula:
\[ \text{Surface Area} = \pi r^2 + \pi r l \]
where:
- \( r \) is the radius of the base of the cone,
- \( l \) is the slant height of the cone.
In this case, you provided the height of the cone as 16 cm, but we need to find the radius and slant height.
To find the radius, you're given the height (16 cm) and the vertical height (h = 17 cm). Assuming "17 cm" refers to the height of the cone, it wouldn't directly help here since we need the radius to calculate the surface area.
Let's solve it assuming \(r\) is unknown, and using the Pythagorean theorem to find the slant height (\(l\)):
- If the vertical height \(h = 16\) cm is given and we assume the cone's radius is \(r = 17\) cm: \[ l = \sqrt{r^2 + h^2} = \sqrt{17^2 + 16^2} = \sqrt{289 + 256} = \sqrt{545} \]
Given that the radius is likely provided by a misunderstanding in the text (here, the height is ordinarily less than the slant height), let’s use standard conventions:
So, let's calculate the surface area:
- Let \( r = 17 \) cm
- \( h = 16 \) cm
- \( l = \sqrt{r^2 + h^2} = \sqrt{17^2 + 16^2} = \sqrt{289 + 256} = \sqrt{545} \).
Now, substituting into the surface area formula:
The surface area \(A\) becomes: \[ A = \pi (17^2) + \pi (17)(\sqrt{545}) \] Calculating \( 17^2 = 289 \): \[ A = \pi (289) + 17\pi \sqrt{545} \]
The final answer for the surface area in terms of \(\pi\) is: \[ \text{Surface Area} = 289\pi + 17\pi \sqrt{545} \text{ cm}^2 \]
You should replace these assumptions if contextually the dimensions are established differently; provide the problem context for further clarity if needed!
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