:L "a or Zar' = v (3) Substitute [21mm we get [3) in (1) and simplify to 21"" = arr) h 1 2V ' 2": + r (4) h = 21' oh h ' a lie. agrees with the result or our first 50 Practice Problems 2- The "Ohm\" 0' an Open box with a square base is 4.000 cm\". Find the'dimensions of the box if the material used to make the box is a minimum. 3. Find the volume of the largest right circular cylinder that can be cut from a circular cone of radius 6 cm and height 9 cm. 4. Find the height of the right circularlcylinder of maximum volume that can be inscribed in a sphere of radius 15 cm. 5, Find the dimensions of the largest rectangle that can be im- cribed in the ellipse 9::1 + 16yl = 144. The sides of the rectangle are parallel to the axes of the ellipse. \"u v elk Practice Problems 6. An isosceles trapezoid has a lower base of 16 cm and the sloping sides are each 8 cm. Find the width of the upper base for greatest area. 7. A trapezoidal gutter is to be made from a sheet of tin 22 cm wide by bending up the edges. If the base is 14 cm wide, what width across the top gives the greatest carrying capa- city? 8. The sum of the bases and altitude of an isosceles trapezoid is . 36 em. Find the altitude if the area is to be a maximum. 9. A building with a rectangular base is to be constructed on a lot in the form of a right triangle with legs 18 m and 24 m. If the building has one side along the hypotenuse of the triangle nd the dimensions of the base of the building to maxiinum floor area. .A . . u 9- I.' :. A- I... Ant-IRMA our] Aiuir'n infra fllr