MathMaster logo

MathMaster

  1. Home
  2. general
  3. mathematician euler understood that it is possible to discover the number of edges in a solid with the number of faces and
Question

Mathematician Euler understood that it is possible to discover the number of edges in a solid with the number of faces and vertices. In this way, it was possible to understand the total volume of three-dimensional objects. In an area of Maria's house, a cube-shaped aquarium will be built, which will be installed in the courtyard of her house. However, Maria would like to know the total volume of this cube, to know how much water she will use. As data, we have: the aquarium will be 1 meter high, 50 cm long and 70 cm deep. Regarding the total volume of the cube, analyze the following sentences: I- The volume will be 0.35 m3, that is, 350 liters. II- The volume will be 35 m3, that is, 3,500 liters. III- The volume will be 0.35 m3, that is, 3,500 liters

224

likes
1120 views

Answer to a math question Mathematician Euler understood that it is possible to discover the number of edges in a solid with the number of faces and vertices. In this way, it was possible to understand the total volume of three-dimensional objects. In an area of Maria's house, a cube-shaped aquarium will be built, which will be installed in the courtyard of her house. However, Maria would like to know the total volume of this cube, to know how much water she will use. As data, we have: the aquarium will be 1 meter high, 50 cm long and 70 cm deep. Regarding the total volume of the cube, analyze the following sentences: I- The volume will be 0.35 m3, that is, 350 liters. II- The volume will be 35 m3, that is, 3,500 liters. III- The volume will be 0.35 m3, that is, 3,500 liters

Expert avatar
Santino
4.5
107 Answers
\text{Given: Height } = 1 \, \text{meter}, \, \text{Length } = 0.5 \, \text{meters}, \, \text{Depth } = 0.7 \, \text{meters}

### Calculation of Volume

The formula to calculate the volume of a rectangular prism is:

V = \text{Height} \times \text{Length} \times \text{Depth}

Substitute the given values:

V = 1 \, \text{meter} \times 0.5 \, \text{meters} \times 0.7 \, \text{meters}

V = 0.35 \, \text{cubic meters (m}^3)

Since 1 cubic meter equals 1,000 liters:

0.35 \, \text{m}^3 \times 1,000 \, \text{liters/m}^3 = 350 \, \text{liters}

### Analysis of Statements

I. The volume will be 0.35 m³, that is, 350 liters.
- **Correct**. The volume is 0.35 cubic meters, which is equivalent to 350 liters.

II. The volume will be 35 m³, that is, 3,500 liters.
- **Incorrect**. The correct volume is 0.35 cubic meters, not 35 cubic meters, and 35 cubic meters would convert to 35,000 liters.

III. The volume will be 0.35 m³, that is, 3,500 liters.
- **Incorrect**. The volume of 0.35 cubic meters is correct, but it equals 350 liters, not 3,500 liters.

### Conclusion

The only correct statement is:

I. The volume will be 0.35 m³, that is, 350 liters.

\textbf{Answer: } \text{Volume = 0.35 cubic meters or 350 liters}

Frequently asked questions (FAQs)
What is the value of the median, given that the sum of three consecutive terms in an arithmetic sequence is 45?
+
What is the value of the square root function at x = 16?
+
What are the solutions to the quadratic equation x^2 + 4x + 3 = 0?
+
New questions in Mathematics
what is 9% of 307
Find the equation of the normal to the curve y=x²+4x-3 at point(1,2)
what is 3% of 105?
You are planning to buy a car worth $20,000. Which of the two deals described below would you choose, both with a 48-month term? (NB: estimate the monthly payment of each offer). i) the dealer offers to take 10% off the price, then lend you the balance at an annual percentage rate (APR) of 9%, monthly compounding. ii) the dealer offers to lend you $20,000 (i.e., no discount) at an APR of 3%, monthly compounding.
There were no defectives in a sample of 1 light bulb does this sample provide sufficient evidence that in the warehouse with millions of light bulbs fewer than 10% are defective?
find f(x) for f'(x)=3x+7
Let A, B, C and D be sets such that | A| = |C| and |B| = |D|. Prove that |A × B| = |C × D|
Using the bank and exact method, calculate the interest on capital 10000 at 12% annual nominal interest rate for the period from 15.3. 2016 until 10/10/2016
In a laboratory test, it was found that a certain culture of bacteria develops in a favorable environment, doubling its population every 2 hours. The test started with a population of 100 bacteria. After six hours, it is estimated that the number of bacteria will be:
Buffalo Company makes and sells shampoo. Each unit requires $1.40 labor costs, material costs per unit are $0.90 and other variable costs are $0.30. It sells shampoo for $4.45 to retailers. Fixed costs are $15,000. It sold 25,000 units in the current month. What is the Break-Even point in units? What is the Break-Even point in dollars? What is the contribution margin of Buffalo Company?
Derivative of 2x
Two particles of electrical charges Q1=3.8×10-⁶C and q,=4.4×10-⁶C are separated in vacuum by a distance of 4.0.10-⁸ m. Since K=9.0.10⁹ N.m²/C², the intensity of the interaction force between them, in newtons, is?
Nancy is a waitress at Seventh Heaven Hamburgers. She wants to estimate the average amount each table leaves for a tip. A random sample of 5 groups was taken and the amount they left for a tip (in dollars) is listed below: $11.00 $8.00 $6.00 $3.00 $7.00 a.) Find a 90% confidence interval for the average amount left by all groups. (*round to the nearest cent*) $ < μ < $ b.) If the sample size were larger, with everything else remaining the same, would the margin of Error increase or decrease? Decrease Increase c.) If the Confidence level were 95% instead of 90%, would the range (size) of the Confidence Interval be larger or smaller? Larger Smaller
A company dedicated to the manufacture of shirts sells the units at a price of $40, the cost of each shirt is $24, a commission is paid for the sale of a unit of shirt of $2 and its fixed costs are $3500 Determine the marginal contribution
Perform operations with the polynomials P(x) = x3 and Q(x) = 2x2 + x – 3x3 : a) P(x) - Q(x)
A group of 17 people spent 9 days on vacation and spent R$776.34 on barbecue meat and the bill needs to be divided as follows: 6 people stayed for 9 days, 7 people stayed for 4 days, and 2 people stayed for 5 days and 2 people stayed 3 days, how much does each group have to pay for the days they stayed?
write in set builder notation { 1,3,9,27,81,243,...}
Convert (324)𝑓𝑖𝑣𝑒 into base-ten
-Please answer to the following questions: What is the price elasticity of demand? Can you explain it in your own words? What is the price elasticity of supply? Can you explain it in your own words? What is the relationship between price elasticity and position on the demand curve? For example, as you move up the demand curve to higher prices and lower quantities, what happens to the measured elasticity? How would you explain that? B-Assume that the supply of low-skilled workers is fairly elastic, but the employers’ demand for such workers is fairly inelastic. If the policy goal is to expand employment for low-skilled workers, is it better to focus on policy tools to shift the supply of unskilled labor or on tools to shift the demand for unskilled labor? What if the policy goal is to raise wages for this group? Explain your answers with supply and demand diagrams. Make sure to properly cite and reference your academic or peer-reviewed sources (minimum 2).
An invoice for €2,880 plus default interest of €48.40 was paid on October 28th. Interest rate 5.5%. When was the bill due?

You might be interested in