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Assuming it is a right cone, use Pythagoras - slant height = hypotenuse, other two sides = radius of base, and height.
Use the equation for the volume of a cone, replace the known height and volume, and solve the resulting equation for the radius.
By means of Pythagoras' theorem providing you are given the radius and perpendicular height of the cone
Volume of a cone = 1/3*pi*radius2*height To find the radius make it the subject of the above formula.
Uisng the lateral area and tha radius, you should be able to find the height of the cone. Using the height and radius as the legs of a right triangle, use the Pythagorean Theorem. The hypotenuse is the slant height.