The cost of polishing the total surface area of a solid cone at ₹ 0.50 per cm² is ₹ 5632, and the circumference of its base is 176 cm. What is the height of the cone? (Use π = 22/7)

Correct option is C

​$$\textbf{Given:} \\\text{Cost} = 5632 \\\text{Rate} = 0.50 \text{ per cm}^2 \\\text{Circumference} = 176 \text{ cm} \\\pi = \frac{22}{7} \\\textbf{Concept Used:} \\\text{Surface area of cone} \\\textbf{Formula Used:} \\\text{TSA} = \frac{\text{Cost}}{\text{Rate}} \\2\pi r = \text{Circumference} \\\text{TSA of cone} = \pi r (r + l) \\l^2 = r^2 + h^2 \\\textbf{Solution:} \\\text{TSA} = \frac{5632}{0.50} = 11264 \\2 \times \frac{22}{7} \times r = 176 \\r = 28 \\\frac{22}{7} \times 28 (28 + l) = 11264 \\88(28 + l) = 11264 \\28 + l = 128 \\l = 100 \\100^2 = 28^2 + h^2 \\10000 = 784 + h^2 \\h^2 = 9216 \\h = 96 \\\textbf{Final Answer:} \\96 \text{ cm}$$​​