Question

Talisa plans a 30-foot deep pond. While digging, she hits rock 25 feet down. How can Talisa modify

the radius to maintain the original volume of the pond?

Answer 1

9514 1404 393

Answer:

multiply the radius by √1.2 ≈ 1.0954

Explanation:

Let the original depth and radius be represented by 30 and r. Let the modified depth and radius be represented by 25 and r'. Assuming the pond is uniform depth, the formula for the volume of a cylinder applies. The volume of a cylinder is given by ...

V = πr²h

In this application, we want the original and modified volumes to be the same.

πr²(30) = π(r')²(25)

(r')² = r²(30/25) = r²(6/5)

r' = r√(6/5)

The radius can be multiplied by √1.2 to maintain the original volume of the pond.