Answer:
\(\text{The equivalent equations are }s=\frac{LA}{\pi r}\text{ and }r=\frac{LA}{\pi s}\)
Option A and D are correct.
Step-by-step explanation:
Given the formula for the lateral area of a right cone is
LA = πrs
where r is the radius of the base and s is the slant height of the cone.
we have to select the equations which equivalent to the above
we have to solve the given equation for variable s and r.
Solve for s
\(LA = \pi rs\)
\(\text{Divide throughout by }\pi r\)
\(\frac{LA}{\pi r} = \frac{\pi rs}{\pi r}\)
\(s=\frac{LA}{\pi r}\)
Solve for r
\(LA = \pi rs\)
\(\text{Divide throughout by }\pi s\)
\(\frac{LA}{\pi s} = \frac{\pi rs}{\pi s}\)
\(r=\frac{LA}{\pi s}\)
\(\text{Hence, the equivalent equations are }s=\frac{LA}{\pi r}\text{ and }r=\frac{LA}{\pi s}\)
Option A and D are correct.
