Q. 223.8( 22 Votes )

# From a solid cyli

Answer :

Height of solid cylinder = h = 8 cm

Radius of solid cylinder = r = 6 cm

Volume of solid cylinder = πr2h

= 3.14 × 6 × 6 × 8 cm3

= 904.32 cm3

Curved Surface area of solid cylinder = 2πrh

Height of conical cavity = h = 8 cm

Radius conical cavity = r = 6 cm

Volume of conical cavity = 1/3 πr2h

= 1/3 × 3.14 × 6 × 6 × 8 cm3

= 301.44 cm3

Let l be the slant height of conical cavity

l2 = r2 + h2

l2 = (62 + 82) cm2

l2 = (36 + 64) cm2

l2 = 100 cm2

l = 10 cm

Curved Surface area of conical cavity = πrl

Since, conical cavity is hollowed out from solid cylinder, so, volume and total surface area of remaining solid will be found out by subtracting volume and total surface area of conical cavity from volume and total surface area of solid cylinder.

Volume of remaining solid = Volume of solid cylinder – Volume of conical cavity

Volume of remaining solid = 904.32 cm3 – 301.44 cm3

= 602.88 cm3

Total surface area of remaining solid = Curved Surface area of solid cylinder + Curved Surface area of conical cavity + Area of circular base

Total surface area of remaining solid = 2πrh + πrl + πr2

= πr × (2h + l + r)

= 3.14 × 6 × (2 × 8 + 10 + 6) cm2

= 3.14 × 6 × 32 cm2

= 602.88 cm2

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