1. Three solid spheres of RDX whose diameters are 2 cm, 12 cm and 16 cm are fused to form a bigger
sphere of RDX. This solid sphere slipped into a cylindrical container of radius 9 cm and height
18 cm full of concentrated nitric acid, by the terrorists handling this project. Show that the acid spilled
out of the cylinder is twice the acid left inside.
Answers
Given : Three solid spheres of RDX whose diameters are 2 cm, 12 cm and 16 cm are fused to form a bigger sphere of RDX.
This solid sphere slipped into a cylindrical container of radius 9 cm and height 18 cm full of concentrated nitric acid,
To Find : Show that the acid spilled out of the cylinder is twice the acid left inside.
Solution:
Three solid spheres of RDX whose diameters are 2 cm, 12 cm and 16 cm
Radius = 1 , 6 , 8 cm
Volume = (4/3)πR³
Total Volume = (4/3)π (1³ + 6³ + 8³)
= (4/3)π (1³ + 6³ + 8³)
= (4/3)π (729)
= (4/3)π9³
Radius of Larger RDX = 9 cm
Diameter of larger RDX = 18 cm
Acid Slipped = Volume of RDX = (4/3)π9³ =12x9²π cm³
Volume of Cylinder = πr²h
= π9²(18)
= 18x9²π cm³
Acid = 18x9²π cm³
Acid left = 18x9²π - 12x9²π = 6x9²π cm³
Acid Slipped = 12x9²π cm³ = 2 x 6x9²π cm³
=> Acid Slipped = 2 x Acid left inside
acid spilled out of the cylinder is twice the acid left inside.
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