Question

Talisa plans a 6-foot deep pond. While digging, she hits rock 5 feet down. How can Talisa modify the radius to maintain the origional volume of the point. *I just dont know the steps to get the answers

Answer 1

Answer:

The new radius r' should be 1.1 times the original planned radius ( rp ).

Step-by-step explanation:

Solution:-

- We will assume the geometry of the pond is modeled as a cylinder with base modeled as a circle with radius ( r ) and the planned height of the ( hp = 6 feet ).

- The volume V of a cylindrical pond is given by:

                              V = π*r^2*h

- Talisa had planned a depth hp = 6 feet, The planned volume with planned radius ( rp ) was:

                              Vp = π*rp^2*6

- However, she hit a rock at h' = 5 feet, So what change must he make to the radius of the pond such that she achieves the planned volume of the pond.

                              V =  π*r'^2*h'

Where, r' is the new radius of the pond:

                             Vp = V

                             π*rp^2*6 =  π*r'^2*5

                             ( r' / rp )^2 = 6 / 5

                             r' / rp = √6 / 5

                             r' / rp = 1.09544

                            r' = 1.1*rp

- The new radius r' should be 1.1 times the original planned radius ( rp ).