Import Question JSON

Current Question (ID: 8779)

Question:

$\text{A thin wire has a length of 21.7 cm and a radius of 0.46 mm. The volume of the wire to correct significant figures is:}$

Options:

1. $0.15 \text{ cm}^3$
2. $0.1443 \text{ cm}^3$
3. $0.14 \text{ cm}^3$
4. $0.144 \text{ cm}^3$

Solution:

$\text{Hint: Use the rule to multiply significant digits.}$ $\text{Step 1: Find the volume of the wire.}$ $\text{The volume of the wire is given by } V = \pi r^2 l$ $\text{Convert radius to cm: } 0.46 \text{ mm} = 0.46 \times 10^{-1} \text{ cm} = 0.046 \text{ cm}$ $V = 3.14 \times (0.46 \times 10^{-1})^2 \times 21.7 = 0.144 \text{ cm}^3$ $\text{Step 2: Use the rule for the multiplication of significant digits}$ $\text{The final answer should have the least number of significant figures as the given numbers have.}$ $\text{Length: 21.7 cm has 3 significant figures}$ $\text{Radius: 0.46 mm has 2 significant figures}$ $\text{Therefore, the volume of the wire is } 0.14 \text{ cm}^3 \text{ (rounded to 2 significant figures).}$ $\text{Hence, option (3) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}