In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14 cm and the other is hemispherical with diameter 21 cm.
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding stimulus
Model Answer
(i) Area of base of cylindrical cup:
Radius = 7/2 = 3.5 cm
Area of base = $\pi r^2 = \frac{22}{7} \times 3.5 \times 3.5 = \mathbf{38.5 \text{ cm}^2}$
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(ii) Capacity of hemispherical cup:
Radius = 21/2 = 10.5 cm
Capacity = $\frac{2}{3}\pi r^3 = \frac{2}{3} \times \frac{22}{7} \times 10.5 \times 10.5 \times 10.5$
$= \frac{2}{3} \times \frac{22}{7} \times 1157.625 = \mathbf{2425.5 \text{ cm}^3}$
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(iii) Curved surface area of cylindrical cup:
Radius = 3.5 cm, Height = 14 cm
CSA = $2\pi r h = 2 \times \frac{22}{7} \times 3.5 \times 14 = \mathbf{308 \text{ cm}^2}$
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Source: Surface Areas and Volumes, Chapter 12
Explanation
- For (i), only the base circle area is needed — not total surface area.
- For (ii), a hemisphere's volume is $\frac{2}{3}\pi r^3$; "capacity" means volume, so use this formula.
- For (iii), CSA of cylinder = $2\pi rh$ (excludes top and bottom circles).
- Always halve the diameter to get radius before substituting. Use $\pi = \frac{22}{7}$ unless told otherwise.