Q. 223.8( 20 Votes )

Answer :

Height of solid cylinder = h = 8 cm

Radius of solid cylinder = r = 6 cm

Volume of solid cylinder = πr^{2}h

= 3.14 × 6 × 6 × 8 cm^{3}

= 904.32 cm^{3}

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 πr^{2}h

= 1/3 × 3.14 × 6 × 6 × 8 cm^{3}

= 301.44 cm^{3}

Let l be the slant height of conical cavity

l^{2} = r^{2} + h^{2}

⇒ l^{2} = (6^{2} + 8^{2}) cm^{2}

⇒ l^{2} = (36 + 64) cm^{2}

⇒ l^{2} = 100 cm^{2}

⇒ 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 cm^{3} – 301.44 cm^{3}

= 602.88 cm^{3}

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 + πr^{2}

= πr × (2h + l + r)

= 3.14 × 6 × (2 × 8 + 10 + 6) cm^{2}

= 3.14 × 6 × 32 cm^{2}

= 602.88 cm^{2}

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PREVIOUSA solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and the height of the cone is 4 cm. The solid is placed in a cylindrical tub full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and its height is 9.8 cm, find the volume of the water left in the tub.NEXTFrom a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.

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