Answer:
[tex]\begin{gathered} V=835.59\text{ m}^3 \\ S.A.=547.11\text{ m}^2 \end{gathered}[/tex]
Explanation:
Given:
Radius(r) = 7.2 m
Slant height(l) = 17 m
To find:
The volume and surface area
Let's go ahead and determine the height(h) of the cone using the Pythagorean theorem as seen below;
[tex]\begin{gathered} l^2=h^2+r^2 \\ 17^2=h^2+7.2^2 \\ 289=h^2+51.84 \\ h^2=289-51.84 \\ h^2=237.19 \\ h=\sqrt{237.19} \\ h=15.4\text{ m} \end{gathered}[/tex]
So the height(h) of the cone is 15.4 m
Let's go ahead and solve for the Volume(V) of the cone using the below formula;
[tex]\begin{gathered} V=\frac{\pi r^2h}{3} \\ =\frac{3.14*7.2^2*15.4}{3} \\ =835.59\text{ m}^3 \end{gathered}[/tex]
So the volume of the cone is 835.59 m^3
We can go ahead and determine the surface area(S.A.) of the cone as seen below;
[tex]\begin{gathered} S.A.=\pi r^2+\pi rl \\ =\pi r(r+l) \\ =3.14*7.2(7.2+17) \\ =22.608(24.2) \\ =547.11\text{ m}^3 \end{gathered}[/tex]
So the surface area of the cone is 547.11 m^2
