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 ?

Question

Philoid · Accepted Answer

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