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Surface Areas and Volumes
RD Sharma
CBSE
Grade 10

Question:

A gulab jamun contains sugar syrup up to about $30\%$ of its volume. Find approximately how much syrup would be found in $45$ gulab jamuns, each shaped like a cylinder with two hemispherical ends with length $5\text{ cm}$ and diameter $2.8\text{ cm}$.

Step-by-Step Solution

Key Concept: $r = 1.4\text{ cm}, h_{cyl} = 5 - 2.8 = 2.2\text{ cm}$. Volume of 1 jamun $= \pi r^2 h + \dfrac{4}{3} \pi r^3 = \pi r^2\left(h + \dfrac{4}{3} r\right) = \dfrac{22}{7} \times 1.96 \times \left(2.2 + 1.867\right) = 6.16 \times 4.067 = 25.05\text{ cm}^3$. Vol of 45 jamuns $= 45 \times 25.05 = 1127.25\text{ cm}^3$. Syrup Vol $= 30\% \times 1127.25 = 338.18\text{ cm}^3 \approx 338\text{ cm}^3$.
$r = 1.4\text{ cm}, h = 2.2\text{ cm}$. Vol of 1 jamun $= \dfrac{22}{7} \times 1.96 \times \left(2.2 + \dfrac{5.6}{3}\right) = 6.16 \times \dfrac{12.2}{3} = 25.05\text{ cm}^3$. [1.5 Marks]
Vol of 45 jamuns $= 45 \times 25.05 = 1127.25\text{ cm}^3$. [1.0 Mark]
Syrup Vol $= 0.30 \times 1127.25 = 338.18 \approx 338\text{ cm}^3$. [0.5 Mark]

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🎯 Official CBSE Marking Scheme:
Calculating volume of 1 gulab jamun $= 25.05\text{ cm}^3$: 1.5 Marks
Calculating total volume of 45 jamuns $= 1127.25\text{ cm}^3$: 1.0 Mark
Evaluating 30% syrup volume $\approx 338\text{ cm}^3$: 0.5 Mark

Correct Answer:
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