SSC MTS 2024 PYQ — Question 10

The correct answer is Option 4 i.e. 9 : 7.

Let original cone height = h and radius = R

The small (cut) cone has height = $3h\over4$ (it is cut at $h\over4$ from the base)

Since cones are similar, the radius of the smaller cone = $3R\over4$

Curved surface area of cone = πrl,

where l is the slant height

CSA of a smaller cone = $\pi({3R\over4})({3l\over4})$ = $\pi rl \times{ ({9\over16})}$

CSA of frustum = πRl - $\pi Rl \times{ ({9\over16})}$ = πRl(1 - $9\over16$) = $\pi Rl \times{ ({7\over16})}$

Required ratio = ${9\over16}\over{7\over16}$ = $9\over7$ = 9 : 7