Question

A solid metallic cuboid of dimensions 10 cm × 5 cm × 3 cm is melted and cast into a box of thickness .5 cm without lid. If the outer measurements of base of box are 12 cm and 5 cm.find the height of the box

Answer 1

volume of cuboid = length * breadth * height

= 10*5*3

= 150 cm cube

volume of cuboid = volume of box

dimensions of box= l= 12 and 11.5cm

= b = 5 and 4.5cm

= h = H and H-0.5 cm *

volume of box = 12*5*H - 11.5*4.5*H-0.5

= 60H - (11.5 * 4.5 * H-0.5)

according to question= 150=60H - (51.75H - 25.875)

150 = 60H - 51.75H + 25.875

150- 25.875 = 8.25H

124.125 = 8.25H

H = 12412.5/ 825

H = 15.04cm

so height of the box is 15.04 cm.


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