Question

A solid cylinder has a total surface area of 462 cm^2. If its curved surface area is one third of its total surface area. Find the height of the cone.

Answer 1

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T.S.A.=462 cm^2

=>πr^2h=462

=> 22/7×r^2h=462

=>hr^2=462×7/22

=>hr^2=147

=>h=147/r^2. ________ equation 1

and

curved surface area= 1/3 total surface area

=>2πrh=1/3×462

=>2×22/7×rh=154

=>44/7×rh=154

=>rh= 154×7/44

=>rh=245/10

=>rh=24.5

=>h=24.5/r __________ equation 2

now

putting the value of h in equation 2 from equation 1

147/r^2=24.5/r

=>147r=24.5r^2

=> 24.5r^2=147r

=>24.5r^2-147r=0

=> r(24.5r-147)=0

=>24.5r-147=0/r

=>r=147×10/245

=>r= 1470/245

=>r=6

now putting the value of r in equation 2

h=24.5/r

=>h=24.5/6

=>h=245/60

=>h= 49/12 cm. 

and

L=√h^2+√r^2

=>L=√(49/12)^2+√(6)^2

=>L=√2401/144+√36

=>L= √2401+5184/144

=>L=√7585/144

=>L=√7585/144

=>L=√52.67

=>L=7.25 cm answer.......

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