Answer:
0.000013527m^3
Explanation:
volume of the cone is expressed as shown;
[tex]V\text{ = }\frac{1}{3}\pi r^2h[/tex]r is the radius = 20mm
h is the height
Given slant height l = 38mm
Using the pythagoras theorem;
l^2 = h^2 + r^2
38^2 = h^2 + 20^2
h^2 = 38^2 - 20^2
h^2 = 1,444 - 400
h^2 = 1044
h = \sqrt[1044]
h = 32.31mm
Get the volume;
[tex]\begin{gathered} V\text{ = 1/3 }\times\text{ 3.14 }\times20^2\text{ }\times32.31 \\ V\text{ = 1/3 }\times3.14\times400\times32.31 \\ V\text{ = }\frac{40,581.36}{3} \\ V\text{ = }13,527.12\operatorname{mm}^3 \end{gathered}[/tex]Converting to m^3
1mm^3 = 1e-9m^3
13,527mm^3 = x
x = 13,527 * 1e-9
x = 0.000013527m^3
Hence the volume of the cone to nearest cubic meters is 0.000013527m^3
