Numerical answer
A right circular cone has base radius 7 cm and height 24 cm. It is cut by a plane parallel to its base at a height of 12 cm above the base. Find the volume (in cm³) of the frustum that remains, taking π = 22/7.
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Answer: 1078
Volume of the full cone = 1/3 × π × 7² × 24 = 392π.
The cut is halfway up, so the small cone removed from the top is similar with scale factor 1/2 (height 12, radius 3.5). Its volume = (1/2)³ × 392π = 49π.
Frustum = 392π − 49π = 343π = 343 × 22/7 = 1078 cm³.
Tip: Similar solids scale in volume by the cube of the linear ratio — much faster than the frustum formula.
The cut is halfway up, so the small cone removed from the top is similar with scale factor 1/2 (height 12, radius 3.5). Its volume = (1/2)³ × 392π = 49π.
Frustum = 392π − 49π = 343π = 343 × 22/7 = 1078 cm³.
Tip: Similar solids scale in volume by the cube of the linear ratio — much faster than the frustum formula.
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