Question

visitors to the bird oasis aviary are given a cone - shaped cup filled with birdseed to feed the birds. the cup has a radius of 3 inches and can hold 37.7 cubic inches of birdseed. what is the height of the cup? the volume of a cone with radius r and height h is ( v=\frac{1}{3}pi r^{2}h ). write your answer as a whole number or decimal rounded to the nearest tenth. inches

Explanation:

Step1: Substitute the given values into the formula

Given \(V = 37.7\), \(r = 3\), and the formula \(V=\frac{1}{3}\pi r^{2}h\). Substitute these values: \(37.7=\frac{1}{3}\times\pi\times3^{2}\times h\).

Step2: Simplify the equation

First, calculate \(3^{2}=9\). Then \(\frac{1}{3}\times\pi\times9 = 3\pi\). The equation becomes \(37.7 = 3\pi h\).

Step3: Solve for \(h\)

We know that \(\pi\approx3.14\). So \(3\pi\approx3\times3.14 = 9.42\). Then \(h=\frac{37.7}{9.42}\).
\(h=\frac{37.7}{9.42}\approx4.0\)

Answer:

\(4.0\)