Question

Write an expression to represent the amount of water remaining in a 4th tank which is the same size

as the others and which contains 512 spheres. Leave your expression in terms of pie

Answer 1

Amount of water = x³- 4/3 π (x/2)³

Explanation:

Let's assume there is a cubic tank, we have 512 spheres in it. Now we have to write an expression in terms of pie.

Let's suppose:

x = edge of the tank

volume of a cube = x³

volume of sphere = 4/3 π r³

where, r = radius of a sphere.

So, we have 512 spheres in total, it means there are 8 spheres in a single row.

(8)³ = 512

It means radius of a single sphere will be = x/16, where x represents the edge of the cubic tank.

Radius of sphere = x/16

So, the formula to calculate the amount of water in the tank will be:

Amount of water in the tank = Volume of cube - Volume of all spheres.

Amount of water = x³ - 512 x ( 4/3 π r³)

Amount of water = x³- 512 x ( 4/3 π (x/16)³)

Amount of water = x³- 512 x ( 4/3 π x³/4096)

Amount of water = x³- 4/3 π x³/8

Amount of water = x³- 4/3 π (x/2)³

Hence, this will be the expression required.