Question

sig figures, conversions, density test form b

1. the volume of a metal object is found to be 45 cm³. its mass is 449 grams. what is the density of this substance?

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1. if a day on venus is 3.87×10⁷ sec long. how many earth days are in a venus - day?

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1. silver has a density of 10.5 g/cc. a solid piece of silver with a volume of 21.4 cc would have a mass of?

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if the silver has a value of $127 per ounce what is the value of this piece?
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1. how many inches are in 4.94 meters answer in 2 significant figures

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1. if soup in germany has nutritional info of 8.9 calories per ml, how many ounces would you need to get the daily requirements of 2000 calories?

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Explanation:

Step1: Recall density formula

The formula for density $
ho$ is $
ho=\frac{m}{V}$, where $m$ is mass and $V$ is volume. Given $m = 449$ g and $V=45$ cm³.
$
ho=\frac{449}{45}$

Step2: Calculate density

$
ho\approx9.98$ g/cm³

Step3: For Venus - Earth day conversion

We know that 1 Earth - day has 24 hours, 1 hour has 60 minutes and 1 minute has 60 seconds. So 1 Earth - day has $24\times60\times60 = 86400$ s.
Let $n$ be the number of Earth - days in a Venus - day. Given a Venus - day is $3.87\times 10^{5}$ s long. Then $n=\frac{3.87\times 10^{5}}{86400}$

Step4: Calculate number of Earth - days

$n=\frac{3.87\times 10^{5}}{86400}\approx4.48$

Step5: For silver mass calculation

Using $
ho=\frac{m}{V}$, we can solve for $m$. Given $
ho = 10.5$ g/cc and $V = 21.4$ cc. Then $m=
ho V=10.5\times21.4$

Step6: Calculate silver mass

$m = 10.5\times21.4 = 224.7$ g. Since 1 ounce = 28.35 g, the number of ounces of silver is $\frac{224.7}{28.35}\approx7.93$ ounces.

Step7: Calculate silver value

If silver is $127 per ounce, the value of the silver piece is $127\times7.93$

Step8: Calculate value

$127\times7.93 = 1007.11$

Step9: For meter - inch conversion

We know that 1 inch = 2.54 cm and 1 m=100 cm. So 1 m=$\frac{100}{2.54}$ inches.
For 4.94 m, the number of inches is $4.94\times\frac{100}{2.54}$

Step10: Calculate inches

$4.94\times\frac{100}{2.54}\approx194.49$ inches. Rounding to 2 significant figures gives 190 inches.

Step11: For soup volume calculation

If there are 8.9 calories per ml and we need 2000 calories. First, find the volume in ml. Let $V$ be the volume in ml. Then $V=\frac{2000}{8.9}$

Step12: Convert ml to ounces

Since 1 ounce $\approx$ 29.57 ml. The number of ounces is $\frac{\frac{2000}{8.9}}{29.57}$

Step13: Calculate ounces

$\frac{\frac{2000}{8.9}}{29.57}=\frac{2000}{8.9\times29.57}\approx7.6$ ounces

Answer:

1. The density of the metal object is approximately 9.98 g/cm³.
2. There are approximately 4.48 Earth - days in a Venus - day.
3. The mass of the silver piece is 224.7 g and its value is $1007.11.
4. There are 190 inches in 4.94 m (to 2 significant figures).
5. You would need approximately 7.6 ounces of soup to get 2000 calories.