- Slant height=l=3ft
- Radius=r=2ft
We know
[tex]\boxed{\sf \star TSA_{(Cone)}=\pi r(r+\ell)}[/tex]
[tex]\\ \sf\longmapsto TSA_{(Old\:Cone)}=2
\dfrac{22}{7}\times 2(2+3)[/tex]
[tex]\\ \sf\longmapsto TSA_{(Old\:Cone)}=\dfrac{44}{7}(5)[/tex]
[tex]\\ \sf\longmapsto TSA_{(Old\:Cone)}=\dfrac{220}{7}[/tex]
[tex]\\ \sf\longmapsto TSA_{(Old\:Cone)}=31.4ft^2[/tex]
Now
- New slant height =2(3)=6cm
- New radius=2(2)=4cm
[tex]\\ \sf\longmapsto TSA_{(New\:Cone)}=\dfrac{22}{7}\times 4(4+6)[/tex]
[tex]\\ \sf\longmapsto TSA_{(New\:Cone)}=\dfrac{88}{7}(10)[/tex]
[tex]\\ \sf\longmapsto TSA_{(New\:Cone)}=\dfrac{880}{7}[/tex]
[tex]\\ \sf\longmapsto TSA_{(New\:Cone)}=125.7cm^2[/tex]
So
[tex]\\ \sf\longmapsto \dfrac{TSA_{(New\:Cone)}}{TSA_{(Old\:Cone)}}=\dfrac{125.7}{31.4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{TSA_{(New\:Cone)}}{TSA_{(Old\:Cone)}}=\dfrac{4}{1}[/tex]
[tex]\\ \sf\longmapsto\underline{\boxed{\bf{ {TSA_{(New\:Cone)}}:{TSA_{(Old\:Cone)}}=4:1}}}[/tex]
