A mountain is in the shape of a cone whose height is about 5.4 kilometers and whose base radius is about 3 kilometers. Approximate the volume of the mountain in cubic kilometers…

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asked Jun 25, 2023 2.8k views

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Paul Riker · Answer 1 · 2023-06-29T10:02:55+0000

Given that a mountain is in the shape of a cone, the figure is shown below

Since the mountain have the shape of a cone, we use the volume of a cone to find the volume of the mountain

The formula for the volume, V, of a cone is

$\begin{gathered} V=(1)/(3)\pi r^2h \\ \text{Where r is the radius} \\ h\text{ is the height} \end{gathered}$

Given that

$\begin{gathered} h=5.4\operatorname{km} \\ r=3\operatorname{km} \end{gathered}$

Substitute the values into the formula for the volume of a mountain

$\begin{gathered} V=(1)/(3)\pi r^2h \\ V=(1)/(3)*\pi*3^2*5.4=50.8938\approx51\operatorname{km}^3\text{ (nearest whole number)} \\ V=51\operatorname{km}\text{ (nearest whole number)} \end{gathered}$

Hence, the volume, V, of the mountain is 51km³ (nearest whole number)

A mountain is in the shape of a cone whose height is about 5.4 kilometers and whose-example-1

A mountain is in the shape of a cone whose height is about 5.4 kilometers and whose base radius is about 3 kilometers. Approximate the volume of the mountain in cubic kilometers…

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