A gardener purchases a ceramic planter in the shape of a hem

A gardener purchases a ceramic planter, in the shape of a hemisphere, fir a small batch of leftover annuals. The volume of a hemisphere is modeled by the function V=2/3 r³. 1. Write a model for the radius as a function of volume. 2. The label on the planter says that it holds approximately 134 cubic inches of potting soil. What is the radius of the planter, rounded to the nearest inch? Use 3.14 for .

Solution

V = 2/3 r³

==> r³ = 3V/(2)

==> r = [3V/(2)]^1/3

2) Given V = 134 in³

==> r = [3(134)/(2)]^1/3

==> r = [3(134)/(2*3.14)]^1/3

==> r = [64.01274]^1/3

==> r = 4.0003

==> radius of the planter = 4 inches.