Q. 21

Answer :

A solid is in the form of a right circular cone mounted on a hemisphere.

Let r be the radius of hemisphere and cone

Let h be the height of the cone

Radius of hemisphere = r = 2.1 cm

Volume of hemisphere = 2/3 πr^{3}

= 2/3 × 22/7 × 2.1 × 2.1 × 2.1 cm^{3}

= 19.404 cm^{3}

Height of cone = h = 4 cm

Radius of cone = r = 2.1 cm

Volume of cone = 1/3 πr^{2}h

= 1/3 × 22/7 × 2.1 × 2.1 × 4 cm^{3}

= 18.48 cm^{3}

Volume of solid = Volume of hemisphere + Volume of cone

= 19.404 cm^{3} + 18.48 cm^{3} = 37.884 cm^{3}

The solid is placed in a cylindrical tub full of water in such a way that the whole solid is submerged in water, so, to find the volume of water left in the tub we need to subtract volume of solid from cylindrical tub.

Radius of cylinder = r’ = 5 cm

Height of cylinder = h’ = 9.8 cm

Volume of cylindrical tub = πr’^{2}h’ = 22/7 × 5 × 5 × 9.8 cm^{3}

= 770 cm^{3}

Volume of water left in the tub = Volume of cylindrical tub – Volume of solid

Volume of water left in the tub = 770 cm^{3} – 37.884 cm^{3} = 732.116 cm^{3}

∴ Volume of water left in the tub is 732.116 cm^{3}

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PREVIOUSA wooden article was made by scooting out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is 20 cm and its base is of diameter 7 cm, find the total surface area of the article when it is ready.NEXTFrom a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8 cm and of base radius 6 cm is hollowed out. Find the volume of the remaining solid. Also, find the total surface area of the remaining solid. [Take π = 3.14.]