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The diagram above shows a cone with the dimensions of its...

The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone.

The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone.

A.

12cm

B.

15cm

C.

18cm

D.

24cm

E.

30cm

Correct answer is D

Considering the smaller and larger triangle, these two are similar triangles. Hence, 

If the height of the smaller triangle = h, 

12h = 6h + 72 \implies 6h = 72

h = 12 cm

\therefore The height of the cone = 12 + 12 = 24 cm