a solid right cylinder is 18 cm high and the radius of the base is 7 cm .two equal right cones are drilled on the plane faces of the cylinder , height of each cone being1/3rd the height of the cylinder and the radius of base of each cone being equal to base of the cylinder . find the total surface  area of the remaining solid

Dear Student,

The following figure can be drawn based on the statements given.


 Total surface area of the solid left = total surface area of cylinder - 2×Total surface area of cones
Total Surface area of cyclinder= 2πr(h+r)putting values in the aboave formula we getTotal Surface area of cyclinder= 2×227×7×(18+7)=44×25=1100

Total surface area of the cone=πr2+πrl
227×7×7+227×7×lwe can find l using pythagoras theoreml2=r2+h2l2=72+62l2=85l=85l=9.22Total surface area of cone227×7×7+227×7×9.2222×7+22×9.22356.84Total surface area of two cones2×356.84=713.68

Total surface area of solid left
=1100-713.68
=386.32

Regards,

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