Mathematics

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

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: Option D
Explanation

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