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Surface Areas and Volumes
NCERT Exemplar Ch 11
CBSE_NCERT_EXEMPLAR_CH11
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: Radius $r = 1.4\text{ cm}$. Height of cylinder $h = 5 - 2(1.4) = 2.2\text{ cm}$. Volume of 1 gulab jamun $= \text{Vol(cylinder)} + 2 \times \text{Vol(hemisphere)}$.
Stepwise Solution:

Radius $r = 1.4\text{ cm}$. Cylinder height $h = 5 - 2.8 = 2.2\text{ cm}$. [0.5 Mark]

Volume of 1 gulab jamun $= \pi r^2 h + \dfrac{4}{3}\pi r^3 = \pi r^2 \left(h + \dfrac{4}{3}r\right) = \dfrac{22}{7} \times (1.4)^2 \times \left(2.2 + \dfrac{5.6}{3}\right) = 6.16 \times \dfrac{12.2}{3} = 25.05\text{ cm}^3$. [1.5 Marks]

Total volume of 45 gulab jamuns $= 45 \times 25.05 = 1127.25\text{ cm}^3$.
Volume of syrup $= 30\% \text{ of } 1127.25 = 0.30 \times 1127.25 \approx 338\text{ cm}^3$. [1.0 Mark]

Marking Scheme:

• Cylinder height $h = 2.2\text{ cm}$: 0.5 Mark
• Volume of 1 gulab jamun $= 25.05\text{ cm}^3$: 1.5 Marks
• Total volume of 45 gulab jamuns and $30\%$ syrup volume $\approx 338\text{ cm}^3$: 1.0 Mark

Correct Answer:
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