John planned a birthday party for his younger sister with his friends. They decided to make some birthday caps by themselves and to buy a cake from a bakery shop. For these two items, they decided the following dimensions:
Cake: Cylindrical shape with diameter 24 cm and height 14 cm.
Cap: Conical shape with base circumference 44 cm and height 24 cm.
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding stimulus
Model Answer
(a) Paper used for 4 caps:
Base circumference = 44 cm → 2πr = 44 → r = 7 cm
Slant height, $l = \sqrt{r^2 + h^2} = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25$ cm
Curved surface area of 1 cap = πrl = (22/7) × 7 × 25 = 550 cm²
Paper for 4 caps = 4 × 550 = 2200 cm²
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(b) Weight of cake to order:
Radius of cake = 24/2 = 12 cm, height = 14 cm
Volume = πr²h = (22/7) × 12 × 12 × 14 = 6336 cm³
Weight = 6336 ÷ 650 × 100 g = 974.8 g ≈ 1 kg
They should order a 1 kg cake.
Source: Surface Areas and Volumes, NCERT Class 10 Maths
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Explanation
- For the cap, only the curved surface area (πrl) is used — no base, since caps are open at the bottom.
- Always find slant height $l$ using $\sqrt{r^2+h^2}$ before computing CSA of a cone.
- For part (b), compute the full cylinder volume, convert to grams, then round up to the nearest 0.5 kg (since they need at least that much cake). 974.8 g exceeds 0.5 kg, so they must order 1 kg.