Question

A pillar is cylindrical base and conical top. The base diameter of the pillar is 1.4m.The slant height of a conical part is 2.6m.The height of the cylindrical part is 3m.Find the cost of painting the pillar at the rate of Rs.20/sq,m.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Cost\:of\:painting\:pillar=378.4\:rupees}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{given : }} \\ \tt{: \implies Slant\:height\:of\:conical\:part= 2.6 \: m} \\ \\ \tt{: \implies Height \: of \: cylindrical \: part =3 \: m} \\ \\ \tt{: \implies Radius \: of \: cone = Radius \: of \: cylinder = 0.7 \: m} \\ \\ \red{ \underline \bold{To \: Find : }} \\ \tt{: \implies Cost\: of \: painting\:pillar =?}$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt{: \implies C.S.A\: of \: cone = \pi rl }\\ \\ \tt{: \implies C.S.A\: of \: cone = \frac{22}{7} \times 0.7 \times 2.6} \\ \\ \tt{: \implies C.S.A \: of \: cone =22 \times 0.26} \\ \\ \green{\tt{: \implies C.S.A \: of \: cone =5.72 \: { m}^{2}}} \\ \\ \bold{As \: we \: know \: that} \\ \tt{: \implies C.S.A\: of \: cylinder = 2\pi rh }\\ \\ \tt{: \implies C.S.A\: of \: cylinder= 2\times \frac{22}{7} \times 0.7\times 3} \\ \\ \tt{: \implies C.S.A\: of \: cylinder =22 \times 0.6} \\ \\ \green{\tt{: \implies C.S.A \: of \: cylinder = 13.2\: { m}^{2}}} \\ \\ \bold{for \: Total \: C.S.A} \\ \tt{: \implies C.S.A \: of \: pillar= C.S.A \: of \: (cone + cylinder)} \\ \\ \tt{: \implies C.S.A \: of \: pillar = 5.72+ 13.2} \\ \\ \green{\tt{: \implies C.S.A \: of \: pillar =18.92\:{m}^{2}}}$

$\bold{cost \: of \: 1 \: {m}^{2} \: painting \: pillar =20 \: rupees} \\ \tt{: \implies cost \: of \: painting \: \: 18.92 {m}^{2} = 20 \times 18.92} \\ \\ \green{\tt{: \implies cost \: of \: painting \: \:pillar = 378.4 \: rupees}}$