A solid metallic cylinder is cut into two identical halves along its height. The diameter of the cylinder is 7 cm and the height is 10 cm. Find:
(a) The total surface area of both the halves.
(b) The total cost of painting the two halves at the rate of ₹30 per cm².
(Use π = 22/7)
Diameter (d) = 7 cm
Radius (r) = d/2 = 7/2 = 3.5 cm
Height (h) = 10 cm
(a) When the cylinder is cut along its height, two new rectangular surfaces are formed.
Total surface area of both halves = Total surface area of the cylinder + Area of two rectangles
⇒ Total surface area = 2πr(h + r) + 2(h × d)
⇒ Total surface area = 2 × \frac{22}{7} × 3.5 × (10 + 3.5) + 2 × 10 × 7
⇒ Total surface area = 22 × 13.5 + 140
⇒ Total surface area = 297 + 140
⇒ Total surface area = 437 cm²
Therefore, the total surface area of both halves is 437 cm².
(b) Cost of painting = Area × Rate
⇒ Cost = 437 × ₹30
⇒ Cost = ₹13,110
Therefore, the total cost of painting is ₹13,110.
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