What is the slant height of cone if the total surface area of cone is 17776 meter cube and the radius of cone is 56 m.?
Answers
GIVEN:
\longrightarrow\sf{Total\: surface\: area \: of \: cone = 17776\: m^3 }⟶Totalsurfaceareaofcone=17776m3
\longrightarrow\textsf{Radius of the cone = 56 cm}⟶Radius of the cone = 56 cm
TO FIND:
\longrightarrow\sf\red{Slant \: height \: of \: the \: cone}⟶Slantheightofthecone
SOLUTION:
Let the slant height be "l"
We know that,
\longmapsto\underline{\boxed{\sf\green{Total\: surface\: area \: of \: cone = \pi r [ r + l ] }}}⟼Totalsurfaceareaofcone=πr[r+l]
Substitute the values.
\implies\sf 17776 = \pi r [ r + l ]⟹17776=πr[r+l]
\implies\sf 22/7 \times 56 [ 56 + l ] = 17776⟹22/7×56[56+l]=17776
\implies\sf 22 \times 8 [ 56 + l ] = 17776⟹22×8[56+l]=17776
\implies\sf 176 [ 56 + l ] = 17776⟹176[56+l]=17776
\implies\sf 56 + l = \dfrac{17776}{176}⟹56+l=17617776
\implies\sf 56 + l = 101⟹56+l=101
\implies\sf l = 101 - 56⟹l=101−56
\implies\sf l = 45⟹l=45
\therefore\underline\textsf{ The slant height of the cone is 45m. }∴ The slant height of the cone is 45m.
Right circular cone
Solve for slant height
r Radius =56
A Surface area =
17776