Question

a new gardening misting system uses spherical misters placed throughout the garden. each mister has a volume of approximately 900 cubic inches. find the radius of each mister using the formula for the volume of a sphere, ( v=\frac{4}{3}pi r^{3} ). use 3.14 for ( pi ) and round your answer to the nearest tenth, if necessary. and use the keypad to enter the answer in the box. the radius of each sphere is approximately ( square ) inches.

Explanation:

Step1: Substitute the values into the formula

Given \(V = 900\) and \(\pi=3.14\), substitute into \(V=\frac{4}{3}\pi r^{3}\). So, \(900=\frac{4}{3}\times3.14\times r^{3}\).

Step2: Solve for \(r^{3}\)

First, simplify the right - hand side: \(\frac{4}{3}\times3.14 = 4.1867\) (approx). Then the equation becomes \(900 = 4.1867r^{3}\). Solving for \(r^{3}\), we get \(r^{3}=\frac{900}{4.1867}\approx215\).

Step3: Find \(r\)

Take the cube root of \(r^{3}\). \(r=\sqrt[3]{215}\approx6.0\) (using a calculator for \(\sqrt[3]{215}\)).

Answer:

\(6.0\)