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Surface Areas and Volumes
RD Sharma
CBSE
Grade 10

Question:

An ice cream cone consists of a cone surmounted by a hemisphere. The radius of the cone is $3.5\text{ cm}$ and its height is $12\text{ cm}$. Find the total volume of the ice cream.

Step-by-Step Solution

Key Concept: Volume $= \dfrac{1}{3} \pi r^2 h + \dfrac{2}{3} \pi r^3 = \dfrac{1}{3} \times \dfrac{22}{7} \times 12.25 \times (12 + 7) = \dfrac{1}{3} \times 38.5 \times 19 = 243.83\text{ cm}^3$.
$\text{Cone Vol} = \dfrac{1}{3} \times \dfrac{22}{7} \times 12.25 \times 12 = 154\text{ cm}^3$. [1.0 Mark]
$\text{Hemisphere Vol} = \dfrac{2}{3} \times \dfrac{22}{7} \times 42.875 = 89.83\text{ cm}^3$. [1.0 Mark]
$\text{Total Volume} = 154 + 89.83 = 243.83\text{ cm}^3$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Calculating cone volume $= 154\text{ cm}^3$: 1.0 Mark
Calculating hemisphere volume $= 89.83\text{ cm}^3$: 1.0 Mark
Evaluating total ice cream volume $= 243.83\text{ cm}^3$: 1.0 Mark

Correct Answer:
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