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WAEC Mathematics 2025 Paper
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© africaexams.com
Question : 27
Total: 50
The diagram above shows a cone with the dimensions of its frustum indicated. Calculate the height of the cone.
24 cm
15 cm
8 cm
12 cm
Validate
Solution:
Triangles OAD is similar to OBC
OA
AD
\frac{\text{OA}}{\text{AD}}
AD
OA
= OB
But
OB
BC
\frac{\text{OB}}{\text{BC}}
BC
OB
= OA + OB
Height of the cone is OB
Let OA = x;
OB = 12 + x
x
6
\frac{\text{x}}{6}
6
x
=
(
12
+
x
)
12
\frac{(12 + x)}{12}
12
(
12
+
x
)
Hence
x
6
\frac{\text{x}}{6}
6
x
=
(
12
+
x
)
12
\frac{(12 + x)}{12}
12
(
12
+
x
)
⇒ 12x = 6x + 72
6x = 72 ⇒ x = 12 cm
Height of cone is DB = 12 + x = (12 + 12) cm = 24 cm
© africaexams.com
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