The diagram above shows a cone with the dimensions of its frustum indicated. Calculate the height of the cone.
Attached Figure / Diagram
A
24 cm
B
15 cm
C
8 cm
D
12 cm
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Triangles OAD is similar to OBC
\(\frac{\text{OA}}{\text{AD}}\) = OB
But \(\frac{\text{OB}}{\text{BC}}\) = OA + OB
Height of the cone is OB
Let OA = x;
OB = 12 + x
\(\frac{\text{x}}{6}\) = \(\frac{(12 + x)}{12}\)
Hence \(\frac{\text{x}}{6}\) = \(\frac{(12 + x)}{12}\) ⇒ 12x = 6x + 72
6x = 72 ⇒ x = 12 cm
Height of cone is DB = 12 + x = (12 + 12) cm = 24 cm
Source: Myschool Past Questions Archive (Record #75841)