[tex]\begin{gathered} \text{LSA}\approx312m^2 \\ V\approx794m^3 \end{gathered}[/tex]
1) Note that this solid, is a cross-sectioned cone. We can find the Lateral Surface Area, using this formula:
[tex]LSA=\pi\cdot s\cdot(R+r)_{}[/tex]
Where R, is the biggest radius, s for the slant height, r for the smallest radius.
2) So, plugging the measures into that we can write out:
[tex]\text{LSA}=\pi\cdot9.63(6.20+4.10)=311.61m^2\approx312m^2[/tex]
Note that we have rounded it off to the nearest whole. So now, let's find the volume of that solid:
[tex]V=\frac{\pi h}{3}(R^2+Rr+r^2)[/tex]
Plugging into that the given dimensions:
[tex]\begin{gathered} V=\frac{\pi h}{3}(R^2+Rr+r^2) \\ V=\frac{\pi\cdot9.4}{3}(6.2^2+6.2\cdot4.1+4.1^2) \\ V\approx794m^3 \end{gathered}[/tex]
Note the volume in cubic meters.
And that is the answer
