Question

a cone - shaped container has a height of 240 in. and a radius of 150 in. the cone is filled with a liquid chemical. the chemical evaporates at a rate of 12,000 in³ per week. how many weeks will it take for all of the chemical to evaporate? use 3.14 to approximate pi. enter your answer in the box

Explanation:

Step1: Calculate the volume of the cone

The formula for the volume of a cone is $V = \frac{1}{3}\pi r^{2}h$. Given $r = 150$ in, $h = 240$ in, and $\pi\approx3.14$.
Substitute the values into the formula:
$V=\frac{1}{3}\times3.14\times150^{2}\times240$
First, calculate $150^{2}=22500$.
Then, $\frac{1}{3}\times3.14\times22500\times240 = 3.14\times7500\times240$ (since $\frac{22500}{3}=7500$)
$3.14\times7500\times240 = 3.14\times1800000 = 5652000$ cubic inches.

Step2: Calculate the number of weeks

The evaporation rate is $12000$ $in^{3}$ per week. To find the number of weeks $t$, we use the formula $t=\frac{V}{\text{rate}}$.
Substitute $V = 5652000$ and rate $= 12000$:
$t=\frac{5652000}{12000}=471$

Answer:

471