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26. Three cylinders each of height 16 cmandradius of base 4 cm are placed on a planeso that each cylinder touches the othertwo. What is the volume of the regionenclosed between the three cylinders?(A) 98(43-) cm(A)(B)(C)(D)98(4V3-Ď) cm 398(2-3-m)cm?98( /3-n)cm128(2V3-x) cm 3 |
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Answer» Draw the cross section of the region. The cylinders will be represented by circles.Join the centers of the circles to form an equilateral triangle with a side of length 2r = 8cm Area of an equilateral triangle = (√3/4)a²a = 8Area = 16√3 cm² There are three equal sectors included in this area, each with an angle of 60°Area of the three sectors = 3×(60/360)×π×4²Area of the sectors = 8π cm² Area between the circles = (16√3 - 8π)cm²= 8(2√3 - π)cm² Volume between the cylinders = Area × height= 8(2√3 - π)cm² × 16= 128(2√3 - π)cm² |
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