Question

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the surface area of a cone is given by the formula \\(s = \pi r l + \pi r^2\\). solve the formula for \\(l\\).

\\(l = s - r^2\\)
\\(l = s + r^2\\)
\\(l = \frac{s}{\pi r} - r\\)
\\(l = \frac{s}{\pi r} + r\\)

Explanation:

State the given equation

We begin with the formula for the surface area of a cone:

$$S = \pi r l + \pi r^2$$

Isolate the term containing l

Subtract \(\pi r^2\) from both sides of the equation:

$$S - \pi r^2 = \pi r l$$

Solve for l

Divide both sides by \(\pi r\) to isolate \(l\):

$$l = \frac{S - \pi r^2}{\pi r}$$

Simplify the expression

Divide each term in the numerator by the denominator:

$$l = \frac{S}{\pi r} - \frac{\pi r^2}{\pi r}$$

$$l = \frac{S}{\pi r} - r$$

Answer:

• (A) \(l = S - r^2\)
• (B) \(l = S + r^2\)
• (C) \(l = \frac{S}{\pi r} - r\) (Correct answer)
• (D) \(l = \frac{S}{\pi r} + r\)