the TSA of a solid right circular cylinder is 231cm^2 if CSA is two - third othe TSA,find the - Maths - Surface Areas and Volumes

Question

the TSA of a solid right circular cylinder is 231cm^2 if CSA is
two - third othe TSA,find the radius of he base

Ayush Jha · Accepted Answer

Let the radius be r and height be h We are given, Total surface area of cylinder = 231 $c m^{2}$ $\Rightarrow 2 π r h + 2 π r^{2} = 231$ ------ (1) Curved surface area $= 2 / 3 \times 231 = 154 c m^{2}$ $\Rightarrow 2 π r h = 154$ ------ (2) Substituting $2 π r h = 154$ in equation (1), we get $154 + 2 π r^{2} = 231 2 π r^{2} = 77 r^{2} = \frac{77}{2} \times \frac{7}{22} \Rightarrow r = \frac{7}{2}$ Substituting the value of r in equation (2), we get $2 π \times \frac{7}{2} \times h = 154 h = \frac{154}{22} \Rightarrow h = 7$

the TSA of a solid right circular cylinder is 231cm^2..if CSA is two - third othe TSA,find the radius of he base.