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 (both the halves).
(b) The total cost of painting the two halves at the rate of ₹ 30 per cm2.
$\Big(\text{use } \pi = \frac{22}{7}\Big)$
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(a) Given,
Diameter of cylinder (d) = 7 cm
Radius of cylinder (r) = $\frac{d}{2} = \frac{7}{2}$ = 3.5 cm
Height of cylinder (h) = 10 cm
Total surface area (both the halves) = Total surface area of cylinder + Area of two rectangles
= [2πr(h + r)] + [2 × (l × b)]
= [2πr(h + r)] + [2 × (h × d)]
= $\Big[2 \times \frac{22}{7} \times 3.5 \times (3.5 + 10) \Big] + [2 \times 10 \times 7]$
= (2 × 22 × 0.5 × 13.5) + 140
= 297 + 140
= 437 cm2.
Hence, total surface area of both the halves = 437 cm2.
(b) Total cost of painting the two halves = Total surface area × Rate
= 437 × 30
= ₹ 13,110.
Hence, total cost of painting the two halves = ₹ 13,110.