Question

the formula for the lateral area of a right cone is ( l.a = pi r s ), where ( r ) is the radius of the base and ( s ) is the slant height of the cone. which are equivalent equations? choose two correct answers.

• ( r = l.a pi s )
• ( s = \frac{l.a}{pi r} )
• ( s = l.a pi r )
• ( r = \frac{l.a}{pi s} )

Explanation:

Step1: Analyze the original formula \( LA = \pi r s \)

We need to solve for \( r \) and \( s \) respectively to find equivalent equations.

Step2: Solve for \( s \)

Starting with \( LA = \pi r s \), divide both sides by \( \pi r \) (assuming \( \pi r
eq 0 \)):
\( s=\frac{LA}{\pi r} \)

Step3: Solve for \( r \)

Starting with \( LA = \pi r s \), divide both sides by \( \pi s \) (assuming \( \pi s
eq 0 \)):
\( r=\frac{LA}{\pi s} \)

Answer:

The two equivalent equations are:

• \( s = \frac{LA}{\pi r} \)
• \( r = \frac{LA}{\pi s} \)