The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone.
Attached Figure / Diagram
A
12cm
B
15cm
C
18cm
D
24cm
E
30cm
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Considering the smaller and larger triangle, these two are similar triangles. Hence,
If the height of the smaller triangle = h,
\(\therefore \frac{h}{6} = \frac{h + 12}{12}\)
\(12h = 6h + 72 \implies 6h = 72\)
\(h = 12 cm\)
\(\therefore\) The height of the cone = 12 + 12 = 24 cm
Source: Myschool Past Questions Archive (Record #23744)