The cost of painting a spherical vessel of diameter 14 cm is Rs. 8008. What is the cost of painting per square centimetre?a)Rs. 8b)Rs. 9c)Rs. 13d)Rs. 14Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Understanding the Problem
To find the cost of painting per square centimetre, we first need to determine the surface area of the spherical vessel.
Calculating the Surface Area
1. Formula for Surface Area of a Sphere:
The surface area $ A $ of a sphere is given by the formula:
$$ A = 4\pi r^2 $$
where $ r $ is the radius of the sphere.
2. Finding the Radius:
Given the diameter of the sphere is 14 cm, the radius $ r $ is:
$$ r = \frac{14 \text{ cm}}{2} = 7 \text{ cm} $$
3. Substituting the Radius:
Now, substituting the radius into the surface area formula:
$$ A = 4 \pi (7)^2 = 4 \pi \times 49 = 196\pi \text{ cm}^2 $$
Approximating $ \pi $ as $ 3.14 $:
$$ A \approx 196 \times 3.14 \approx 615.44 \text{ cm}^2 $$
Calculating the Cost per Square Centimetre
1. Total Cost of Painting:
The total cost to paint the sphere is Rs. 8008.
2. Cost per Square Centimetre:
To find the cost per square centimetre, we divide the total cost by the surface area:
$$ \text{Cost per cm}^2 = \frac{\text{Total Cost}}{\text{Surface Area}} = \frac{8008}{615.44} \approx 13 \text{ Rs/cm}^2 $$
Conclusion
Thus, the cost of painting per square centimetre is approximately
Rs. 13, confirming option 'C' as the correct answer.

Answer

∵ Diameter of the vessel = 14 cm
∴ Radius = 7 cm;

We need to find out the surface area of the spherical vessel;
Surface area of spherical vessel = 4πr²
⇒ 4 × 22/7 × 7²
⇒ 616 cm²

∵ The cost of painting the spherical vessel is Rs. 8008;

∴ Cost of painting per square centimetre = 8008/616 = Rs. 13

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