Question

a solid cylinder has tsa of 462 cm square its csa is one third of its tsa find its radius and height

Answer 1

Answer:) Let the radius and height of the cylinder be, 'r' cm and 'h' cm respectively. Given:) TSA of the cylinder = 462 cm2 ∴ 2p r (r + h) = 462 cm2 .. .(1) Given:) LSA of cylinder = 1/3 × TSA of cylinder... ∴ 2prh =1/3 × 462 = 154 cm2 ... (2) From (1) and (2), we have {2pr(r+h}/{2pr} = 462 cm2 / 154 cm2 (r+h) / h = 3 r = 3h-h=2h r = 2h From (2), we have 2prh =154 cm2 (2 x22rxr) /(7x2)} r = 7cm h = r/2=7/2=3.5cm ∴ Vol of the cylinder = pr2h =22x7x7/3.5=539 cm2.......

Answer 2

total surface area = (2π r h + 2 π r²) = 462 cm²
curved surface area = 2 π r h = 462/3 = 154 cm ²
so,
2π r² = ( 462 - 154)
         =308
⇒ r² = 154 /π
        = 49
⇒ radius = 7 cm
now, 2π r h = 154 cm²
⇒h = 154 /2π r
      = 3.5
height = 3.5 cm