A vessel in shape cuboid contains some water . If three indentical spheres are immersed in the water,the level of water is increased by 2cm. If the area of the base of the cuboid is160cmsquare and its height 12cm ,determine the radius of the spheres.
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Solution:-
Area of the base of cuboid = 160 sq cm
Let the radius of sphere be 'r'
Volume of one sphere = 4/3πr³
Volume of three spheres = 4πr³
Increased height of the cuboidal vessel = 2 cm
Increased volume of the water = (160 ×2) = 320 cu cm
Since the volume is increased after immersing the 3 spheres in the vessel, so increased volume of water will be equal to the volume of three spheres.
⇒ 4πr³ = 320
⇒ 4*22/7*r³ = 320
⇒ r³ = (320*7)88
⇒ r³ = 2240/88
⇒ r³ = 25.45
⇒ r = 2.94 cm
So, the radius of each sphere is 2.94 cm
Answer.
Area of the base of cuboid = 160 sq cm
Let the radius of sphere be 'r'
Volume of one sphere = 4/3πr³
Volume of three spheres = 4πr³
Increased height of the cuboidal vessel = 2 cm
Increased volume of the water = (160 ×2) = 320 cu cm
Since the volume is increased after immersing the 3 spheres in the vessel, so increased volume of water will be equal to the volume of three spheres.
⇒ 4πr³ = 320
⇒ 4*22/7*r³ = 320
⇒ r³ = (320*7)88
⇒ r³ = 2240/88
⇒ r³ = 25.45
⇒ r = 2.94 cm
So, the radius of each sphere is 2.94 cm
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