Question

The radius and the height of a cone are in the ratio 5:12 and its volume is 314mcube, the find its slant height

Answer 1

r = 5x and h = 12x

volume of the cone = 314 cubic m

$\frac{1 }{3} \times 3.14 \times {r}^{2} \times h \: = 314$
${r}^{2} \times h \: = 100 \times 3$
$25 {x}^{2} \times 12 x= 100 \times 3$
${x}^{3} =1 \: \: \: \: \:$
$x = 1$
r =5 h =12

${l}^{2} = {h}^{2} + {r}^{2} \\ = 144 + 25 = 169 \\ \\ l = 13 \: cm$

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Answer 2

let proportionally constant =x
radius =5x
height =12x

volume of cone = pie^2/h/3
314=3.14 (5x)^2 .(12x)/3
100=25×4 (x^3)
x=1
hence
radius =5cm
height =12cm
so,
slant height =root {(12)^2+(5)^2}=13cm
now,
cross section area =pie(r)^2
=3.14×5×5=78.5cm^2
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