thr radius and height of a cylinder are in the ratio 7:2 if the TSA of

1.	thr radius and height of a cylinder are in the ratio 7:2 if the TSA of a cylinder is 2772cm^2 find the radius and height of a cylinder
Answer» ong>Step-by-step EXPLANATION: Given:- The radius and height of a cylinder are in the ratio 7 : 2. The Total surface area of the cylinder (TSA) = 2772cm² To FIND:- The radius of the cylinder. The height of the cylinder. Solution:- Let the COMMON ratio between the radius and height be x So:- The radius of the cylinder (r) = 7x And height of the cylinder (H) = 2x GIVEN, TSA of the cylinder = 2772cm² $\boxed{ \sf TSA \: of \: a \: cylinder = 2\pi r(h + r)}$ $\sf \implies 2\pi r(h + r) = 2772$ $\sf \implies 2\pi \times (7x) \big[2x+ 7x\big] = 2772$ $\sf \implies 2\pi \times 7x \times 9x = 2772$ $\sf \implies 2 \times \dfrac{22}{7} \times 7x \times 9x = 2772$ $\sf \implies 2 \times 22 \times (x) \times 9x = 2772$ $\sf \implies 396x^2 = 2772$ $\sf \implies x^2 = \dfrac{2772}{396}$ $\sf \implies x^2 = 7$ $\sf \implies x = \sqrt{7}$ $\sf The\: radius = 7x = 7 \times \sqrt{7} = 7\sqrt{7}$ $\sf The\: height = 2x = 2\times \sqrt{7} = 2\sqrt{7}$ $\underline{\boxed{\sf The \: radius \: of \: the \: cylinder = 7\sqrt{7}cm}}$ $\underline{\boxed{\sf The \: height \: of \: the \: cylinder = 2\sqrt{7}cm}}$