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The height of a right circular cylinder is \(\frac{10}{5}\) m. Three times the sum of the areas of its two circular faces is twice the area of the curved surface. Find the volume of the cylinder. |
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Answer» Given, Height of cylinder = 10.5 m = 3( A + A) = 2 curved surface area (A = circular area of box) = 3 x 2A = 2(2πrh) = 6πr2 = 4 πrh = r = \(\frac{2h}{3}\) = \(\frac{2\times 10.5}{3}\) = 7 m Volume of cylinder = πr2h = \(\frac{22}{7}\)x 7 x 7 x 10.5 = 1617 cm3 \(\text{Volume of the cylinder is given by:}\\\text{V= area of circular face x height}\equiv A\cdot h\\\text{We know that A }= \pi r^2\text{ and }B\equiv\text{area of curved surface }=2\pi rh\\\text{Therefore:}\\\text{If }3\cdot(2A) = 2B\\\text{then}\\6\pi r^2 = 4\pi rh\implies r=\frac23h\\\text{It follows that:}\\V=\pi\frac49h^3=\pi\frac492^3=\frac{32}9\pi\) |
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