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Yuri pee - 2333 Results
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the problem involves calculating the radius of a cylindrical hole drilled into a prism with a triangular base as described in the diagram we are given the base of the triangular prism has sides of 28 cm 45 cm and 53 cm the height of the prism is 28 cm the circular hole is tangent to the lateral faces of the prism as shown in the figure to find the radius of the cylindrical hole we need to determine the radius of the largest circle that fits inside the triangular base this is known as the incircle of the triangle which is tangent to all three sides of the triangle the formula for the radius of the incircle of a triangle is r fracas where is the area of the triangle and is the semi perimeter of the triangle 1 first calculate the semi perimeter s frac28 45 532 63 textcm 2 now use herons formula to find the area of the triangle a sqrtss as bs c where substitute the values a sqrt6363 2863 4563 53 a sqrt63351810 a sqrt63 times 35 times 18 times 10 sqrt396900 approx 630 textcm2 3 finally calculate the radius r fracas frac63063 10 textcm thus the radius of the perforation is 10 cm but the options provided suggest that 8 cm might average conversation with step mother
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