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.

Answers

Answer 1

Answer:

Both boxes have the same amount of empty space

Explanation:

Given

Cube Box

[tex]Length = 10cm[/tex]

Robert:

1 glass marble

[tex]Diameter = 10cm[/tex]

Susan:

1000 glass marble

[tex]Diameter = 1cm[/tex]

Required

Whose box has more empty space?

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

[tex]Volume = Length^3[/tex]

Substitute 10cm for Length

[tex]Volume = 10^3[/tex]

[tex]Volume = 1000cm^3[/tex]

Next, calculate the volume of Robert's glass

Volume is calculated as:

[tex]Volume = \frac{4}{3}\pi r^3[/tex] ---- Volume of a sphere

Where

r = radius

[tex]r = \frac{1}{2} * Diameter[/tex]

[tex]Diameter = 10cm[/tex] --- Given

Substitute 10 for diameter

[tex]r = \frac{1}{2} * 10cm[/tex]

[tex]r = 5cm[/tex]

So:

[tex]Volume = \frac{4}{3}\pi r^3[/tex]

[tex]Volume = \frac{4}{3} * \frac{22}{7} * 5^3[/tex]

[tex]Volume = \frac{4}{3} * \frac{22}{7} * 125[/tex]

[tex]Volume = 523.8cm^3[/tex]

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

Volume is calculated as:

[tex]Volume = \frac{4}{3}\pi r^3[/tex] ---- Volume of a sphere

Where

r = radius

[tex]r = \frac{1}{2} * Diameter[/tex]

[tex]Diameter = 1cm[/tex] --- Given

Substitute 1cm for diameter

[tex]r = \frac{1}{2} * 1cm[/tex]

[tex]r = 0.5cm[/tex]

Substitute 0.5cm for radius in [tex]Volume = \frac{4}{3}\pi r^3[/tex]

[tex]Volume = \frac{4}{3} * \frac{22}{7} * 0.5^3[/tex]

[tex]Volume = \frac{4}{3} * \frac{22}{7} * 0.125[/tex]

[tex]Volume = 0.5238[/tex]

But there are 1000 glasses.

So, the volume of 1000 glasses is:

[tex]Volume = 0.5238 * 1000[/tex]

[tex]Volume = 523.8cm^3[/tex]

--------------------------------------------------------------------------------------------------------------

For Robert:

[tex]Volume = 523.8cm^3[/tex]

For Susan:

[tex]Volume = 523.8cm^3[/tex]

Since, they have the same volume.

Both boxes have the same amount of empty space

Answer 2

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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Related Questions

Adaptations that help an organism survive appear quickly. True or False? And why

Answers

Answer:

false

Explanation:

is not worth it to do that

According to the theory of natural selection, features that may be passed down help animals adapt to their surroundings more successfully than their kin.

What condition that make organism adaptive?

Adaptations are passable traits that improve an organism's capacity to endure and procreate in a given environment. An organism can manage in harsh settings, locate food and water, and protect itself by adapting.

This is the outcome of a process called natural selection. A species' nature gradually changes as a result of natural selection in order for it to fit into the niche.

If a species becomes extraordinarily well adapted to its habitat and the environment does not change, it can survive for a very long time before going extinct.

Therefore, it is false that, Adaptations that help an organism survive appear quickly.

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Answers

Answer:

Divergent plate boundaries.

Explanation:

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Answers

Answer:

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Explanation:

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Answers

Answer:

Density-independent factor, also called limiting factor, in ecology, any force that affects the size of a population of living things regardless of the density of the population (the number of individuals per unit area).

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Answers

1. RNA is single stranded

2. DNA is double stranded

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6. DNA has a double helix structure

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Answers

Answer:

by signals that the nervous system sends to the brain

Explanation:

What is the role of adenosine triphosphate (ATP) within a cell?

A) Release carbon dioxide
B) Biological molecule that stores energy
C) Use glucose
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Answers

Answer:

Its B. Biological molecule that stores energy

The answer is B.
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Most enzymes are proteins. Many cells make and use an enzyme called catalase to facilitate the decomposition of hydrogen peroxide (H2O2). The products of the decomposition are hydrogen (H2) and oxygen (O2). Stephanie is investigating the structure and function of catalase, and she is comparing catalase to other proteins. What can Stephanie predict will distinguish the structure of catalase from the structures of the other proteins she is studying? A. many regions made entirely of hydrogen and oxygen B. the chemical properties of the peptide bonds C. the types of amino acids it contains D. the sequence of amino acids it contains

Answers

Answer:

The correct answer is - B. the chemical properties of the peptide bonds.

Explanation:

The difference between the structures of catalase from other proteins depends on the chemical properties of the peptide bonds present in between the amino acids which decide the pH and temperature by their disruption. These bonds present between two alpha-amino acids when carboxyl of one amino acid interacts with the amino group of the other to form an amide-type covalent bond.

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Explanation:

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Answer:

The correct words that film in the blanks are;

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Water is a highly polar molecule. Its polarity allows it to form strong intermolecular hydrogen bonds which accounts for the forces of cohesion in the water.

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Answer:

Vice President?

Explanation:

Answer:

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Explanation:

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Answers

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What is the correct order of a food chain containing the following organisms: quail (bird), desert shrub, coyote, snake?

Answers

Answer:

desert shrub - quail - snake - coyote

Explanation:

the quail bird eats the desert shrub, the snake eats the quail, the coyote (a-pex predator in this chain) eats the snake.

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Answers

Answer:

Polysaccharides from cell walls make up the fiber humans eat, while monosaccharides provide the sweetness in foods. As humans eat, chewing breaks down polysaccharides into smaller particles that eventually, through digestion, yield up the simple monosaccharides that can pass into the bloodstream.

Explanation:

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Answers

Answer: wdym

Explanation:

Cells have many parts, each with a different function. ... It also provides a track-like system that directs the movement of organelles and other substances within cells. Endoplasmic reticulum (ER) This organelle helps process molecules created by the cell.

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Answers

Answer:

C

Explanation:

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Answer:

it c

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Answers

Answer:

It is Soldering not peonage

Explanation:

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Answers

It would be D. Fossils fuels.
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Answer: It's C

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A
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Answers

Answer:

C. active transport, because protein pumps are needed to move substances against a concentration difference

Explanation:

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Answers

Answer:

4

Explanation:

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Explanation:

A eukaryotic cell contains membrane-bound organelles such as a nucleus, mitochondria, and an endoplasmic reticulum. Organisms based on the eukaryotic cell include protozoa, fungi, plants, and animals. These organisms are grouped into the biological domain Eukaryota.

Any organism which has a closed membrane for a nucleas is a eukaryotic cell.

(organisms who dont have a nuclear memebrane is called prokaryotic cell)

We have eukaryotic cells as we have nuclear membrane but a bactaria(a prokaryotic cell) doesnt have a nuclear memebrane and all of its nuclear substances are floating insdie it getting jumbled up.

Part D)
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This is on plato and edmentrum. :)​

Answers

Answer:

More force is needed to push the heavier box. Likewise, people who weigh more use more energy to move their bodies than people who weigh less.

Explanation:

copied directly from edmentum/plato

Answer:

More force is needed to push the heavier box. Likewise, people who weigh more use more energy to move their bodies than people who weigh less.

Explanation:

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Answers

Answer/Explanation:

It results in offspring with genetic variation. 2 different mates must be used in sexual reproduction. This is because each person is different since cells are produced and combined differently in the original offsprings. If the two adults were exactly the same, the offspring would have the exact same cell traits. Likewise will be done for the offspring of the two adults. The genes may be similiar to the ones of the adults, but since combined it will not be an exact replica. In the long run sexual reproduction will result in an offspring with slightly different traits or genetic variation.

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Answers

Answer:

extract of beet roots could be used as antifreeze for water systems

Explanation:

In science, a prediction can be defined as a plausible conjecture that is subsequently proved (or rejected) using the scientific method. In other words, a prediction is the expected result obtained if the hypothesis is true. Scientists make predictions based on falsifiable hypotheses which can be tested through experimental and/or observational procedures. In this case, it could be predicted that the extract of beet roots could be used as anti-freeze for water systems in cold climates.

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Answers

Answer:

The correct answer is - the dependent variable.

Explanation:

In any study or research, the variable is that measured or affected by the change occurs lace in an experiment is called the dependent variable. The dependent variable depends on the factors or the variables that are changed in the experiment.

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Answers

Answer:

In DNA replication, cell machinery copies strands of DNA.

Explanation

DNAs, deoxyribonucleic acids, are long-chain, helical macromolecules made of specific sequences of covalently bonded monomers called nucleotides. These contain genetic information essential for growth, reproduction, and cell repair.

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Nucleotides, deriving their name from their nitrogenous bases, pair up to form base pairs. In base-pair formation, Adenine and Thymine form double bonds, while cytosine forms triple bonds with guanine...

DNA polymerase facilitates either DNA synthesis, by adding free nucleases to parent strands -these are first unwound and separated by helicases DNApolys synthesize DNA in 5'-3' direction; due to its restricted movement, there are only two modes of replication: continuous from the point of strand separation, the fork, and discontinuous from the fork.  In continuous replication, DNApolymerase moves uninterrupted along the 3'-5 oriented template, adding nucleotides to the free hydroxyl group at its 3' end to produce the 5'-3' oriented leading strand. During the synthesis of the 3'-5' oriented lagging strand, DNApolymerase  moves backwards along the template from the replication fork; DNA helicase separates the strands, and DNApoly's addition of nucleotides is periodically interrupted while  forming discontinuous Okazaki fragments. Ligase enzymes assemble nucleotide strands of RNA and DNA -here, DNAligase assembles these fragments into continuous strands, producing two identical new helixes formed from a parent and newly replicated strand respectively.

EASY 10 POINTS

Why do plant cells need chloroplasts?

Answers

Answer:

Chloroplasts are organelles found in plant cells and eukaryotic algae that conduct photosynthesis. Chloroplasts absorb sunlight and use it in conjunction with water and carbon dioxide gas to produce food for the plant. In this respect they are similar to mitochondria, but are found only in plants and protista.

Explanation:

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How does this equation represent the law of conservation of energy—that energy cannot be created or destroyed? Consider the role of photosynthesis in your answer.

Answers

Answer:

Energy from the sun goes into making the sugar molecule. This energy is released to make ATP and heat.

Explanation:

6Co2+6H20->C6H12O6(glucose)+6O2(oxygen)

The sugar molecule is created by solar energy. This energy is discharged to produce heat and ATP.

What is the law of conservation of energy?

According to the rule of conservation of energy, energy can only be transformed from one form of energy to another and cannot be generated or destroyed.

This indicates that unless energy is introduced from the outside, a system always has the same quantity of energy. In the situation of non-conservative forces, when energy is changed from mechanical energy to thermal energy yet the overall energy does not change, this is especially perplexing. Energy must be changed from one form to another in order to be used.

In photosynthesis,

6CO + 6H₂O → C₆H₁₂O₆ + 6O₂

Sunlight is used for the light energy required to produce the sugar molecule.

Therefore, the law of conservation of energy is applicable in photosynthesis as energy from the sun is utilized by all living organisms.

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A fungus cell is a prokaryotic cell. True or false?

Answers

A fungus cell is a eukaryotes so it’s false
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