Question

a cone-shaped container is completely filled with liquid. the container has a radius of 60 cm and an height of 210 cm. the liquid is drained from the container at a rate of 1099 $\text{cm}^3$ per hour.
how many hours will it take to drain all of the liquid?
use 3.14 to approximate pi.
enter your answer in the box.

Explanation:

Step1: Calculate cone volume

The formula for the volume of a cone is $V = \frac{1}{3}\pi r^2 h$. Substitute $r=60$, $h=210$, $\pi=3.14$:

$$\begin{align*} V&=\frac{1}{3} \times 3.14 \times 60^2 \times 210\\ &=\frac{1}{3} \times 3.14 \times 3600 \times 210 \end{align*}$$

Step2: Simplify volume calculation

First compute $\frac{1}{3} \times 210 = 70$, then:

$$\begin{align*} V&=3.14 \times 3600 \times 70\\ &=3.14 \times 252000\\ &=791280 \end{align*}$$

Step3: Find drain time

Divide total volume by drain rate:

$$ \text{Time} = \frac{791280}{1099} $$

Step4: Compute final time

Calculate the division:

$$ \text{Time} = 720 $$

Answer:

720