Question

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

Answer 1

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

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

$\pink{➢}$ 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

$\underline{ \boxed{ \sf{➫\: Volume\:of\:cone = \frac{1}{3} {r}^{2} \pi \: h}}}$

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

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

$\sf \:➩ r = \frac{18}{2} \\ \sf \: ➩r = \cancel \frac{18}{2} \\ \sf \: ➩r = 9 \: \: \:$

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

➢ Let's substitute values according to formula

$\sf \: → \frac{1}{3} \times {(9)}^{2}\times 3.14 \times20 \\ \sf→ \frac{1}{3} \times 81 \times 3.14 \times 20 \\ \sf \: → \frac{1}{ \cancel3} \times \cancel{81} \times 3.14 \times 20 \\ \sf→27 \times 3.14 \times 20 \\ \sf \: →1695.6m$

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

Hope it helps !