Question
The volume of a cone is 8192 π cm3. The
height of the cylinder is 35% more than the slant height of the cone. The lateral surface area of the cylinder is 4536 π cm2. If the base area of the cone is 1024 π cm2, then find out the volume of the cylinder (in cm 3).Solution
If the base area of the cone is 1024 π cm2.  π x (radius of the cone)2 = 1024 π   Eq.(i) radius of the cone = 32 cm [Here negative value is not possible.] The volume of a cone is 8192 π cm3. (⅓) x π x (radius of the cone)2 x height of the cone = 8192 π Put Eq.(i) in the above equation. (⅓) x height of the cone = 8 height of the cone = 24 cm  Eq.(ii) (slant height of the cone)2 = (radius of the cone)2 + (height of the cone)2 (slant height of the cone)2 = (32)2 + (24)2 = 1024+576 = 1600 slant height of the cone = 40 cm The height of the cylinder is 35% more than the slant height of the cone. height of the cylinder = (100+35)% of 40 height of the cylinder = 135% of 40 = 54 cm The lateral surface area of the cylinder is 4536 π cm2. 2 x π x radius of the cylinder x height of the cylinder = 4536 π radius of the cylinder x 54 = 2268 radius of the cylinder = 42 Volume of the cylinder = π x (radius of the cylinder)2 x height of the cylinder = π x (42)2 x 54 = (22/7) x 1764 x 54 = 22 x 252 x 54 = 299376 cm3
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