A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts.NCERT Class XMathematics - Exemplar ProblemsChapter _SURFACE AREAS AND VOLUMES
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Volume of the whole cone = 1/3 x 22/7 x 8² x 12 = 804.57 cm³
Radius, r, of small cone is found by similarity:
8/12 = r/6
r = 4cm
Volume of the small cone cut off = 1/3 x 22/7 x 4² x 6 = 100 4/7
Volume of frustum = 804.57 - 100.57 = 704 cm³
The ratio of the two volumes = 100 4/7 : 704 = 1: 7
Radius, r, of small cone is found by similarity:
8/12 = r/6
r = 4cm
Volume of the small cone cut off = 1/3 x 22/7 x 4² x 6 = 100 4/7
Volume of frustum = 804.57 - 100.57 = 704 cm³
The ratio of the two volumes = 100 4/7 : 704 = 1: 7
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