Q31 of 47 Page 1

The height of a cone is 30 cm. From its topside a small cone is cut by a plane parallel to its base. If volume of smaller cone is of the given cone, then at what height it is cut from its base ?


Let r and R be respectively the radii of smaller and bigger cone


& h and H be their respective heights


We know that,





According to the given condition, we have



Putting the values, we get







Since ΔABC ~ Δ ADE







⇒ h = 10cm


Hence, height of the frustum = 30 – 10 = 20cm


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