Import Question JSON

Current Question (ID: 8774)

Question:

$\text{Each side of a cube is measured to be 7.203 m. What are the total surface area and the volume respectively of the cube to appropriate significant figures?}$

Options:

1. $373.7 \text{ m}^2 \text{ and } 311.3 \text{ m}^3$
2. $311.3 \text{ m}^2 \text{ and } 373.7 \text{ m}^3$
3. $311.2992 \text{ m}^2 \text{ and } 373.7147 \text{ m}^3$
4. $373.7147 \text{ m}^2 \text{ and } 311.2992 \text{ m}^3$

Solution:

$\text{Hint: The LEAST number of significant figures in multiplicands of multiplication determines the number of significant figures in the answer.}$ $\text{The number of significant figures in the measured length is 4. The calculated area and the volume should therefore be rounded off to 4 significant figures.}$ $\text{Step 1: Find the total surface area of the cube to appropriate significant figures.}$ $\text{The surface area of the cube} = 6(7.203)^2 \text{ m}^2$ $= 311.299254 \text{ m}^2$ $= 311.3 \text{ m}^2$ $\text{Step 2: Find the volume of the cube to appropriate significant figures.}$ $\text{The volume of the cube} = (7.203)^3 \text{ m}^3$ $= 373.714754 \text{ m}^3$ $= 373.7 \text{ m}^3$

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
}