A right triangle ABC with sides 6cm, 8cm and 10cm is revolved about the side 8cm. Find the volume of solid so formed. If triangle ABC is revolved about the side 6cm, then find the volume of the solid so formed. Also, find the ratio of the volume of the two solids so obtained.
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Step-by-step explanation:
When a right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm, then solid formed is a cone whose height of a cone, h = 8 cm and radius of a cone, r = 6 cm. Slant height of a cone, l = 10 cm
Volume of a cone = 1/3 πr2h = (1/3) x (22/7) x 6 x 6 x 8
⇒ 6336/21 = 301.7 cm3
and curved surface of the area of cone = πrl
⇒ (22/7) x 6 x 10 = 1320/7 = 188.5 cm2
Hence, the volume and surface area of a cone are 301.7 cm3 and 188.5 cm2, respectively.
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