A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is $14\text{ mm}$ and the diameter of the capsule is $5\text{ mm}$. The surface area of the capsule is:
(a) $220\text{ mm}^2$
(b) $140\text{ mm}^2$
(c) $310\text{ mm}^2$
(d) $440\text{ mm}^2$
Step-by-Step Solution
Key Concept: Radius $r = 2.5\text{ mm}$. Cylinder length $h = 14 - 5 = 9\text{ mm}$. Surface Area $= 2 \pi r h + 4 \pi r^2 = 2 \pi r (h + 2r) = 2 \times \dfrac{22}{7} \times 2.5 \times (9 + 5) = 2 \times \dfrac{22}{7} \times 2.5 \times 14 = 44 \times 5 = 220\text{ mm}^2$.
$r = 2.5\text{ mm}, h = 9\text{ mm}$. [0.5 Mark]
$\text{Area} = 2 \pi r(h + 2r) = 2 \times \dfrac{22}{7} \times 2.5 \times 14 = 220\text{ mm}^2$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Finding cylinder height $h = 9\text{ mm}$: 0.5 Mark
Evaluating capsule surface area $= 220\text{ mm}^2$: 0.5 Mark
Correct Answer: $220\text{ mm}^2$