the radius and the height of the cone is 4:3.the area of the base is 154cm^2 .find the curved surface of the cone
Answers
radius and height =.4:3
let the unit of ratio be = x
then,
r=4x
h=3x
slant height ( length) =↓
\begin{gathered}\implies L^{2}=r^{2}+h^{2} \\ \implies l^{2}=4^{2}+3^{2} \\ \implies l^{2}=16+9 \\ \implies l^{2}=25 \\ \implies l=\sqrt25 \\ \implies = l=5 \end{gathered}
⟹L
2
=r
2
+h
2
⟹l
2
=4
2
+3
2
⟹l
2
=16+9
⟹l
2
=25
⟹l=
2
5
⟹=l=5
★ Area of the base = πr^{2}πr
2
\implies 154= \frac{22}{7}×4x^{2}⟹154=
7
22
×4x
2
\implies 4x^{2}=\frac{154×7}{22}⟹4x
2
=
22
154×7
\implies 4x^{2}=7×7⟹4x
2
=7×7
\implies x^{2}=\frac{7×7}{16}⟹x
2
=
16
7×7
\implies x^{2}=\sqrt\frac{7×7}{4×4}⟹x
2
=
4×4
7×7
\implies x=\frac{7}{4}⟹x=
4
7
\implies radius = \frac{7}{4}×4⟹radius=
4
7
×4
\implies radius = 7cm⟹radius=7cm
Now,
slant height ↓
\begin{gathered}\implies \frac{5×7}{4} \\ \implies \frac{35}{4} cm\end{gathered}
⟹
4
5×7
⟹
4
35
cm
→ C.S.A = πrl
\begin{gathered} \implies \frac{22}{7}×7×\frac{35}{4} \\ \implies \frac{776}{4} \\ \implies 192.5cm^{2}\end{gathered}
⟹
7
22
×7×
4
35
⟹
4
776
⟹192.5cm
2
\rule{300}2
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