Question

Areas of three adjacent faces of a solid cuboid are 11 cm sq. , 20 cm sq. , 55 cm sq. respe ctively.The cuboid id melted and recast into spheres each of radius 0.5 cm.Find the number of the spheres,so obtained.

Answer 1

lb=11⇒b=11/l
bh=20⇒h=20/b=20/(11/l)=20l/11
hl=55⇒l=55/h=55/(20l/11)=121/4l
⇒l=121/4l⇒4l²=121⇒l²=121/4⇒l=√121/4=11/2 cm=5.5cm
⇒b=11/l=11×2/11=2cm
⇒h=20/b=20/2=10cm
Volume of the solid cuboid=lbh=5.5×2×10=110cm³
Volume of the sphere=4/3π(1/2)³=4/3×22/7×1/8=11/21cm³
Required no. of spheres=(Volume of the solid cuboid)/(Volume of the sphere)
110/(11/21)=210(Ans.)

Answer 2

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