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A water tank is a cuboid 45cm long, 30cm wide and 26cm high. it contains water to a depth of 21cm. a sphere is placed in the tank and is fully submerged. the water level rises by 1.8cm. volume of a sphere is 4/3 pi r^3 . calculate the radius of the sphere (nearest mm)

Sagot :

The radius of the Sphere that submerged in the water is 178.9 mm.

Volume of the Cuboid:

Volume of cuboid is the total space occupied by the cuboid in a three-dimensional space.

The general form of the Volume of the Cuboid is,

Volume of a cuboid = l × b × h    [cubic units]

Where,

l = length

b = breadth

h = height

Given,

A water tank is a cuboid 45cm long, 30cm wide and 26cm high.

It contains water to a depth of 21cm.

A sphere is placed in the tank and is fully submerged. the water level rises by 1.8cm.

Here we need to find the radius of the Sphere and we have to use the Volume of the sphere as 4/3πr³.

First, we need to find the volume of the water,

For that, we have to take the measurement of it.

l = 45 cm

b = 30 cm

h = 21 cm

( here we have to find the volume of water, so we have take the water depth as its height)

Now, the volume of the water is,

V₁ = 45 x 30 x 21

V₁ = 28350 cm³

After placed the sphere on the tank the water level is increased as 1.8 cm,

So, the new height = 21 + 1.8 = 22.8

Now the new volume is,

V₂ = 45 x 30 x 22.8

V₂ = 30780 cm³

So, the Volume of the increased water level is,

=> 30780 - 28350

=> 2430 cm³

Now we have to consider this as the Volume of the Sphere and calculate the radius through it,

=>  4/3πr³ = 2430

=> r³ = 2430 x 3/4 x π

we know that the value of π = 22/7

So,

=> r³ = 2430 x 3/4 x 22/7

=> r³ = 5727.86

=> r = ∛5727.86

=> r = 17.89

Therefore, the radius of the sphere is 17.89 cm

Now we have to convert it into mm,

=> 1 cm = 10 mm

So,

=> 17.89 cm = 178.9 mm

Therefore, the radius of the sphere is 178.9 mm.

To know more about Volume of Cuboid here.

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