(i) Surface area of the bulb:
Diameter = 7 cm, so radius = 3.5 cm
Surface area = $4\pi r^2 = 4 \times \dfrac{22}{7} \times 3.5 \times 3.5 = 154 \text{ cm}^2$
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(ii) Maximum diameter of bulb leaving 1 cm from each side:
The smallest dimension of the base = 12 cm.
Maximum diameter = 12 − 1 − 1 = 10 cm
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(iii) Area of fabric used (with 2 cm fold on top and bottom):
The fold adds 2 cm on each of the two open ends, so effective height = 17 + 2 + 2 = 21 cm.
Lateral surface area of cuboid (open top & bottom) = Perimeter of base × height
= 2(24 + 12) × 21
= 2 × 36 × 21
= 1512 cm²
OR
Space available inside the lamp:
Volume of cuboid = 24 × 12 × 17 = 4896 cm³
Volume of bulb = $\dfrac{4}{3}\pi r^3 = \dfrac{4}{3} \times \dfrac{22}{7} \times 3.5^3 = \dfrac{4}{3} \times \dfrac{22}{7} \times 42.875 = 179.67 \approx 179.67 \text{ cm}^3$
Space available = 4896 − 179.67 = 4716.33 cm³
Source: Mensuration, Surface Areas and Volumes
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