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प्रश्न
From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8 cm and base radius 6 cm is hollowed out. Find the volume of the remaining solid. Also, find the total surface area of the remaining solid.
उत्तर १
Volume of the solid left = Volume of cylinder - Volume of cone `=pir^2h - 1/3pir^2h = 2/3 xx 22/7 xx 8 xx 6 xx 6 = 603.428 "cm^3'`
The slant length of the cone , `l =sqrt(r^2 + h^2) = sqrt(36+64) = 10 "cm"`
Total surface area of final solid = Area of base circle
उत्तर २
Volume of the solid left = Volume of cylinder - Volume of cone `=pir^2h - 1/3pir^2h = 2/3 xx 22/7 xx 8 xx 6 xx 6 = 603.428 "cm^3'`
The slant length of the cone ,`l =sqrt(r^2 + h^2) = sqrt(36+64) = 10 "cm"`
Total surface area of final solid = Area of base circle + Curved surface area of cylinder +curved area of once`= pirl^2 + 2pirh + pirl = pir (r + 2h +l) = 22/7 xx 6 xx (6 + 16 + 10) = 603.42 "cm"^2`
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