Question

solid cylinder has surface area of 226.38cm2 iyscuved surface area is one third of iyd total surface area find volume of cylinder .solve it step by steps

Answer 1

Hi there !!

T.S.A = 226.38 cm²

Given ,

C.S.A = $\frac{1}{3} T.S.A$
           
          = $\frac{1}{3}$ × 226.38
           
          = 75.46 cm²

We know that,
 T.S.A = 2 × Base area + C.S.A
                          
  2πr² + 2πrh = T.S.A  



2πr² + 75.46 cm²  = 226.38 cm² 

2πr² = 226.38 - 75.46
           
        = 150.92 cm

2× $\frac{22}{7}$ × r² = 150.92 cm

r² = $\frac{150.92*7}{2*22}$

r² = $\frac{1056.44}{44} }$

r² =  24.01

r = √24.01 = 4.9 cm


radius , r = 4.9 cm


C.S.A = 75.46 cm²

2πrh = 75.46 cm²

2 × $\frac{22}{7}$ × 4.9 × h = 75.46

h = $\frac{75.46 *7}{2*4.9*22}$

h = $\frac{528.22}{215.6}$

h = 2.45 metres

Volume of a cylinder = πr²h
                          
                                  = $\frac{22}{7}$ ×4.9 ×4.9 × 2.45
            
                                  = 184.877 cm³