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 volume formula

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

Step2: Simplify the equation

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

Step3: Solve for \(h\)

We know \(\pi\approx3.14\). So \(37.7=3\times3.14\times h\), which is \(37.7 = 9.42h\). Then \(h=\frac{37.7}{9.42}\).

Step4: Calculate the value of \(h\)

\(h=\frac{37.7}{9.42}\approx4.0\)

Answer:

\(4.0\)