Question

Look at this cylinder:

If the radius and height are doubled, then which of the following statements about its surface area will be true?

Answer 1

• Height=h=8cm
• Radius=r=4cm

We know

`\boxed{\sf \star TSA_((Cylinder))=2\pi r(h+r)}`

`\\ \sf\longmapsto TSA_((Old\:Cylinder))=2* (22)/(7)* 4(8+4)`

`\\ \sf\longmapsto TSA_((Old\:Cylinder))=(176)/(7)(12)`

`\\ \sf\longmapsto TSA_((Old\:Cylinder))=(2112)/(7)`

`\\ \sf\longmapsto TSA_((Old\:Cylinder))=301.7cm^2`

Now

• New Radius=2(4)=8cm
• New Height=2(8)=16cm

`\\ \sf\longmapsto TSA_((New\:Cylinder))=2* (22)/(7)* 8(16+8)`

`\\ \sf\longmapsto TSA_((New\:Cylinder))=(352)/(7)(24)`

`\\ \sf\longmapsto TSA_((New\:Cylinder))=(8448)/(7)`

`\\ \sf\longmapsto TSA_((New\:Cylinder))=1204.7cm^2`

So

`\\ \sf\longmapsto (TSA_((New\:Cylinder)))/(TSA_((Old\:Cylinder)))=(1204.7)/(301.7)`

`\\ \sf\longmapsto (TSA_((New\:Cylinder)))/(TSA_((Old\:Cylinder)))=(4)/(1)`

`\\ \sf\longmapsto\underline{\boxed{\bf{ {TSA_((New\:Cylinder))}:{TSA_((Old\:Cylinder))}=4:1}}}`

Hence our correct option is Option C