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प्रश्न
From a soild cylinder of height 20 cm and diameter 12 cm, a conical cavity of height 8 cm and radius 6 cm is hallowed out. Find the total surface area of the remaining solid.
उत्तर
Given, Height of cylinder h1 = 20 cm
Radius of cylinder = `12/2` = 6 cm.
Height of the cone (h2) = 8 cm.
Radius of the cone r = 6 cm.
Total surface area of remaining solid = Curved surface area of cylinder + Curved surface area of cone + Area of the top face of the cylinder
Slant height of the cone (l) = `sqrt("h"_2^2 + "r"^2)`
= `sqrt(8^2 + 6^2)`
= `sqrt(64 + 36)`
= 10 cm.
∴ Curved surface area of cone = πrl
= `22/7 xx 6 xx 10`
= `1320/7` cm2
Curved surface area of cylinder = 2πrh
= `2 xx 22/7 xx 6 xx 20`
= `5280/7` cm2
Area of the top face of the cylinder = πr2
= `22/7 xx 6 xx 6`
= `792/7` cm2
∴ Total surface area of the remaining solid
= `1320/7 + 5280/7 + 792/7`
= `7392/7`
= 1056 cm2
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