a vessel in the shape of a cuboid contains some water if three identical spheres are immersed in - Maths - Surface Areas and Volumes

Question

a vessel in the shape of a cuboid contains some water if three
identical spheres are immersed in water , the level of water is
increased by 2 cm if the area of base of the cuboid is 160 square
cm and its height 12 cm , determine the radius of any of the
spheres

Mayank Bhardwaj · Accepted Answer

Area of the base of the cuboid = 160 cm2 Let the radius of the sphere be r cm $Volume of one sphere = \frac{4}{3} π r^{3}$ Volume of three spheres = 4Ï€r3 Increased height of the cuboidal vessel = 2 cm Increased volume of the water = (160 Ã— 2) cm3 = 320 cm3 Since the volume is increased after immersing the 3 spheres in the vessel, increased volume of water will be equal to the volume of three spheres â‡’ 4Ï€r3 = 320 $\Rightarrow r^{3} = \frac{320}{4 π} \Rightarrow r^{3} = \frac{320}{4 \times \frac{22}{7}} \Rightarrow r^{3} = \frac{320 \times 7}{4 \times 22}$ â‡’ r3 = 25 45 â‡’ r = 2 94 cm Thus, the radius of the spheres is 2 94 cm

a vessel in the shape of a cuboid contains some water . if three identical spheres are immersed in water , the level of water is increased by 2 cm .if the area of base of the cuboid is 160 square cm and its height 12 cm , determine the radius of any of the spheres