A joker's Cup is in the form of a right Circular Cone Of the base radius 7 cm and height 24 cm , Find the area of the sheet required to make 10 such caps.
Answers
Answer:
Here the concept of CSA of Cone has been used. We see that the shape of the solid is a Conical Cap. We know that a Conical Cap is hollow from below so that it can be worn out. This means we have to calculate its Curved Surface Area to find the area of sheet required to make one cap. Firstly we will find the Slant Height of the conical cap and then its CSA. After that we can multiply this area required with 10 to find the area of sheet required to make 10 such caps.
Let's do it !!
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
\bf \underline \red{ \star \:Formula \: used \: \star}
⋆Formulaused⋆
\bf \scriptsize{Slant \: height \: (l) ^{2} = \: h^{2} + r^{2} }Slantheight(l)
2
=h
2
+r
2
\bf \scriptsize{Curved \: surface \: area \: = \pi \: r \: l \: }Curvedsurfacearea=πrl
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
\bf \underline \red{ \star \: Solution\: \: \star}
⋆Solution⋆
\begin{gathered} \bf \scriptsize{As \: we \: kown \: that \: \: \: \: \: \: l^{2} = r^{2} + h^{2} } \\ \bf \scriptsize{ l ^{2} = (7) ^{2} + (24)^{2} = 49 + 576 } \\ \bf \scriptsize \: {l^{2} = 625 } \\ \bf \scriptsize{l = \sqrt{625 } = 25 \: cm } \\ \bf \scriptsize{ \therefore \: curved \: surface \: of \: a \: cap \: = \: \pi \: r \: l } \\ \bf \scriptsize{ = \frac{22}{7} \times7 \times 25 = 22 \times 25 = 550 \: cm^{2} } \end{gathered}
Aswekownthatl
2
=r
2
+h
2
l
2
=(7)
2
+(24)
2
=49+576
l
2
=625
l=
625
=25cm
∴curvedsurfaceofacap=πrl
=
7
22
×7×25=22×25=550cm
2
\begin{gathered} \bf \scriptsize{Area \: of \: sheet \: to \: make \: 10 \: such \: caps \:} \\ \bf \scriptsize{ = 550 \times 10 \: cm ^{2} } \\ \bf \scriptsize{ = 5500 \: cm ^{2} }\end{gathered}
Areaofsheettomake10suchcaps
=550×10cm
2
=5500cm
2
━━━━━━━━━━━