Two students are given cubic boxes, measuring 10 cm on a side. Robert puts a single glass marble with a diameter of 10 cm in the box. Susan puts 1,000 1-cm glass marbles in her box.

1. Whose box has more empty space? Explain.

From the dimensions of glass marble for robert and susan, we can say that; none of the given boxes have more empty space.

We are told that the cubic boxes have a measure of 10 cm for its' sides.

Formula for volume of a cube is;

V = lwh

where;

l is length

w is width

h is height

Thus; V = 10 × 10 × 10

V = 1000 cm³

For Robert;

We are told that he puts a glass marble with a diameter of 10 cm in the box. The glass is usually spherical in shape and the volume of a sphere is;

V = ⁴/₃πr³

Thus;

V_rob = ⁴/₃π × (10/2)³

V_rob = 523.6 cm³

Volume left for rob = 1000 - 523.6

Volume of empty space left for rob = 476.4 cm³

For Susan;

V = ⁴/₃πr³

Thus;

V_sus = ⁴/₃π × (1/2)³ × 1000

V_sus = 523.6 cm³

Volume left for susan = 1000 - 523.6

Volume of empty space left for susan = 476.4 cm³

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Both boxes have the same amount of empty space

Explanation:

Given

Cube Box

Robert:

1 glass marble

Susan:

1000 glass marble

Required

Whose box has more empty space?

First, we need to calculate the volume of the cubic box.

Substitute 10cm for Length

Next, calculate the volume of Robert's glass

Volume is calculated as:

---- Volume of a sphere

Where

r = radius

--- Given

Substitute 10 for diameter

So:

Next, we determine the volume of Susan's 1000 glasses

Volume is calculated as:

---- Volume of a sphere

Where

r = radius

--- Given

Substitute 1cm for diameter

Substitute 0.5cm for radius in

But there are 1000 glasses.

So, the volume of 1000 glasses is:

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For Robert:

For Susan:

Since, they have the same volume.

Both boxes have the same amount of empty space

i think it is dna, i'm not totally sure but i think it might be.