Question

question 1-9 the marine organism, shown below, has a cone - shaped seashell. its volume is 8.3 cubic inches, and the radius of the base is 1.3 inches. what is the height of the seashell from the base to the tip? round your answer to the nearest tenth. inches

Explanation:

Step1: Recall volume formula for cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$, where $V$ is volume, $r$ is the radius of the base, and $h$ is the height. We need to solve for $h$.

Step2: Rearrange the formula for $h$

Starting from $V = \frac{1}{3}\pi r^{2}h$, we can isolate $h$ by multiplying both sides by $3$ and then dividing by $\pi r^{2}$. So $h=\frac{3V}{\pi r^{2}}$.

Step3: Substitute given values

We know that $V = 8.3$ cubic - inches and $r = 1.3$ inches. Substitute these values into the formula: $h=\frac{3\times8.3}{\pi\times(1.3)^{2}}$.

Step4: Calculate the value of $h$

First, calculate the denominator: $(1.3)^{2}=1.69$, and $\pi\times1.69\approx3.14\times1.69 = 5.3066$. Then, $3\times8.3 = 24.9$. So $h=\frac{24.9}{5.3066}\approx4.7$.

Answer:

$4.7$