Question

find the volume of water tank that can be stored in a conical vessel of radius 3 cm and slant height 5 cm



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Answer 1

Step-by-step explanation:

Let slant height, radius and perpendicular height of the conical vessel be l, r and h respectively.

$\therefore \: {l}^{2} = {r}^{2} + {h}^{2} \\ \therefore \: {h}^{2} = {l}^{2} - {r}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: = {5}^{2} - {3}^{2} = 25 - 9 = 16 \\ \therefore \: h = 4 \: cm \\ volume \: of \: water \: tank \\ = volume \: of \:conical \: vessel \\ = \frac{1}{3} \pi \: {r}^{2} h \\ = \frac{1}{3} \times 3.14 \times {(3)}^{2} \times 4 \\ = 3.14 \times 12 \\ = 37.68 \: {cm}^{3}$