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 given values into formula

Given $V = 37.7$, $r = 3$, and the volume formula $V=\frac{1}{3}\pi r^{2}h$. So $37.7=\frac{1}{3}\times\pi\times3^{2}\times h$.

Step2: Simplify the right - hand side

$\frac{1}{3}\times\pi\times3^{2}\times h=\frac{1}{3}\times\pi\times9\times h = 3\pi h$. So the equation becomes $37.7 = 3\pi h$.

Step3: Solve for h

$h=\frac{37.7}{3\pi}$. Using $\pi\approx3.14$, we have $h=\frac{37.7}{3\times3.14}=\frac{37.7}{9.42}\approx4.0$.

Answer:

$4.0$