Question

If you tripled the slant height and radius of a cone, what would be the formula to find the modified surface area?
A.
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B.
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C.
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D.
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Answer 1

Hi, it would be helpful if you post the pictures, too. However, I can lead you given through with the question.

For any cone, the formula for the surface area can be determined by this:



Area of the base + lateral area, so
\(SA=\pi r^2+\pi rs \)
Let's denote \(r_1\) for radius, \(s_1\) for slant height, and \(SA_1\) for surface area all prior to modifications.

Now you are tripling the radius and slant height, so your new values would be
\(r_2=3r_1\)
\(s_2=3s_1\)
Now you can plug them into the SA formula:
\(SA=πr^2+πrs\)
Substitute
\(SA_2=\pi (3r_1)^2+\pi (3r_1)(3s_1)\)\)
Simplify
\(SA_2=9\pi r_{1}^2+9\pi r_1s_1\)
\(SA_2=9(\pi r_1^2+\pi r_1s_1)\)
You can now substitute in the original S.A. (\(SA_1=\pi r_1^2+\pi r_1s_1 \))
\(SA_2=9(SA)\)
\(SA_2=9(\pi r_1^2+\pi r_1s_1)\)