Respuesta :
PROJECT WORK:
Assumption:
For the given cone, assuming
[tex]\begin{gathered} r\text{ = 10 m} \\ h\text{ = 12 m} \end{gathered}[/tex]Slant height of cone is calculated as,
[tex]\begin{gathered} l^2\text{ = r}^2\text{ + h}^2 \\ l^2\text{ = 10}^2\text{ + 12}^2 \\ l^2\text{ = 100 + 144} \\ l^2\text{ = 244} \\ l\text{ = 15.62 m} \end{gathered}[/tex]Required:
Surface area and volume of cone.
Explanation:
The surface area of cone is given as,
[tex]\begin{gathered} Surface\text{ area = }\pi r(l+r) \\ Surface\text{ area = 3.14}\times\text{ 10\lparen15.62 + 10\rparen} \\ Surface\text{ area =3.14}\times\text{ 10\lparen25.62\rparen} \\ Surface\text{ area = 3.14}\times\text{ 256.2} \\ Surface\text{ area = 804.468 m}^2 \end{gathered}[/tex]Volume of cone is calculated as,
[tex]\begin{gathered} Volume\text{ = }\frac{1}{3}\pi r^2h \\ Volume\text{ = }\frac{1}{3}\times3.14\times10\times10\times12 \\ Volume\text{ = }\frac{3768}{3} \\ Volume\text{ = 1256 m}^3 \end{gathered}[/tex]Answer:
Thus the volume of the cone is 1256 cu.m.
The surface area of the cone is 804.468 sq.m.
