A right triangle ABC with its sides 5 cm, 12 cm and 13 cm is revolved about the side 5 cm. Find the volume of the solid so formed. If triangle ABC is revolved about the side 12 cm, find the volume of the solid so formed. Also find the ratio of the volumes of the two solids obtained.
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If triangle ABC is revolved about BC = 5 cm, then the right circular cone is formed with radius = r = AB = 12 cm, and height h = BC = 5 cm
Let V1 be the volume of the cone formed, then
V1 = 1/3 × pi × r^2 × h
= 1/3 × pi × 12 × 12 × 5
= 240 × pi cm^3
Again when triangle ABC is revolved about the side AB, then let V2 be the volume of the cone formed
V2 = 1/3 × pi × r^2 × h
= 1/3 × pi × 5 × 5 × 12 cm^3 [because r = 5 cm and h = 12 cm]
= 100 × pi cm^3
Hence, required ratio
= V2/V1
= 100 × pi / 240 × pi
= 10/24
= 5/12
= 5:12
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