Q. 254.1( 10 Votes )

Answer :

Edge of wooden block (a) = 21 cm

Diameter of hemisphere = edge of cube

Radius = 21/2 = 10.5 cm

Volume of remaining block = Volume of box – Volume of hemisphere

= 6835.5 cm^{3}

Surface area of box = 6a^{2} ………… (1)

Curved surface area of hemisphere = 2πr^{3} ……….. (2)

Area of base of hemisphere ……………….. (3)

So remaining surface area of box = (1) – (2) + (3)

= 2992.5 cm^{2}

Remaining surface area of box=2992.5 cm^{2}

**Volume of remaining block=6835.5 cm ^{3}**

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PREVIOUSA cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the value of water (i) displaced out of the cylinder. (ii) left in the cylinder. NEXTA toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere. If the radius of the base of the cone is 21 cm and its volume is 2/3 of the volume of the hemisphere, calculate the height of the cone and the surface area of the toy.