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

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 ).

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.