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 ).
