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Find the volume of a cone with a diameter of 18 meters and a height of 20 meters

User Andrew Plotkin
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2 Answers

18 votes
18 votes

Final answer:

The volume of the cone is approximately 1,896.48 cubic meters.

Step-by-step explanation:

The volume of a cone can be calculated using the formula,
V = (1/3) × π × r2 × h where r is the radius and h is the height of the cone.

In this case, the diameter of the cone is given as 18 meters, which means the radius (r) will be half of that, i.e. 9 meters. The height (h) is given as 20 meters.

Substituting these values into the formula, we get
V = (1/3) × π × 92 × 20.

Using the value of π as 3.142, the volume of the cone is approximately 1,896.48 cubic meters.

User QuinnChen
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6 votes
6 votes


\huge \sf \color{pink}{A} \color{green}{N} \color{red}{S} \color{blue}{W} \color{orange}{E} \color{grey}{R}


\large \underline{ \boxed{ \sf{✰ \: Important \: points }}}


\pink{➢} Diameter of cone = 18m


\pink{➢}Height of cone = 20m


\pink{➢}A surface of revolution formed by rotating a segment of a line around another line that intersects the first line.


\pink{➢}Cone is basically formed by circular base


\underline{ \boxed{ \sf{➫\: Volume\:of\:cone = (1)/(3) {r}^(2) \pi \: h}}}


\underline{ \boxed{ \sf{ ➪ \: r = radius}}} \\\underline{ \boxed{ \sf{ ➪ \: h = height}}}


\pink{➢} We know that radius is half of diameter


\sf \:➩ r = (18)/(2) \\ \sf \: ➩r = \cancel (18)/(2) \\ \sf \: ➩r = 9 \: \: \:


\pink{➢}Hence radius of cone in data given is 9m

➢ Let's substitute values according to formula


\sf \: → (1)/(3) * {(9)}^(2)* 3.14 *20 \\ \sf→ (1)/(3) * 81 * 3.14 * 20 \\ \sf \: → (1)/( \cancel3) * \cancel{81} * 3.14 * 20 \\ \sf→27 * 3.14 * 20 \\ \sf \: →1695.6m


\pink{➢} Hence volume of cone =1695.6m

Hope it helps !

User Meroz
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2.9k points