Question

If a right circular cone of a certain height has its upper part cut off by a plane passing through the mid-point of its axis and at right angles to it, then the volume of lower portion of the cone and that of the upper portion of the cone will be in the ratio

(a) 7 : 1 

(b) 1 : 7 

(c) 1 : 4 

(d) 4 : 1

Answer 1

Answer: (a) = 7:1 

Let OA = h, OC = r. 

Then, AF = h/2 and by the similarity of triangles AFE and AOC, FE = r/2

∴ \(\frac{Vol.\, of\, portion\, DECB} {Vol.\, of\, cone\, ADE} \)   

= \(\frac{Vol.\, of\, cone\, ABC\, –\, Vol.\, of\, cone\, ADE} {Vol.\, of\, cone\, ADE }\)   

= \(\frac{\frac{1}{3} \pi r^2 h - \frac{1}{24} \pi r^2 h}{\frac{1}{24}\pi r^2 h}\)  = \(\frac{\frac{7}{24}\pi r^2 h}{\frac{1}{24}\pi r^2 h}\) 

= 7:1