Calendar: 1890-1891 Page 762

c ENGINEERING DEPARTMENT The upper and lower faces of mound of earth are rectangles one 12 feet by feet the other 20 feet by feet the sides of the rectangles being parallel each to each and the distance between their planes 30 feet find the number of cubic feet of earth in the mound also the volumes of each of the parts into which the mound is divided by plane half- way between the two rectangles The perpendicular distance between the parallel sides of trapezoid is inches and the lengths of those sides are 16 inches and 10 inches respectively find the volume of the solid figure produced by the revolution of the trapezoid about the longer side about the shorter side hemispherical bowl of radius 12 inches is partly filled with water to the depth of inches find the volume of the water in cubic inches to three places of decimals FIRST SECOND AND THIRD YEARS Crtgonometrj If the angle Β and the sides of triangle are given examine in what cases the triangle is determinate In the case in which there are two solutions prove that the geometric mean between the two values of the third side is equal to the geometric mean between the sum and difference of the two given sides Prove that the area of triangle sides inscribed in circle of radius is abcj and of quadrilateral sides inscribed in circle is -d when 2s a- -6 c- -d Explain the meaning of the proposition that the limit of sin θ θ when θ is and prove it Prove that sin 2Θ 2Θ is less than sin θ θ Prove by induction or otherwise that tan Β י י י $4 $2 when Sx is the sum of the tangents of S2 is the sum of the products of the tangents of two and two together S3 three and three together and so on