question_answer2) A metallic solid sphere of radius \[10.5\text{ }cm\] is melted and recasted into smaller solid cones, each of radius \[3.5\text{ }cm\] and height\[3\text{ }cm\]. How many cones will be made?
question_answer3) From the top of a \[7m\] high building, the angle of elevation of the top of a tower is \[60{}^\circ \] and the angle of depression of its foot is \[45{}^\circ \]. Find the height of the tower.
question_answer4) Draw a right triangle in which the sides (other than the hypotenuse) are of lengths \[4\text{ }cm\] and \[3\text{ }cm\]. Now construct another triangle whose sides are \[\frac{3}{5}\] times the corresponding sides of the given triangle.
question_answer5) If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the sum of its first \[(m+n)\]terms is zero.
question_answer6) Two points A and B are on the same side of a tower and in the same straight line with its base. The angles of depression of these points from the top of the tower are \[60{}^\circ \] and \[45{}^\circ \] respectively. If the height of the tower is 15 m, then find the distance between these points.
question_answer7) The height of a cone is \[30\text{ }cm.\] From its topside a small cone is cut by a plane parallel to its base. If volume of smaller cone is \[\frac{1}{27}\] of the given cone, then at what height it is cut from its base?
