Question:
Shown below is an ice-cream cone completely filled with ice-cream. Assume the top portion (visible portion of ice-cream) is a perfect hemisphere. What is the total mass of the ice-cream in grams? The density of ice-cream is \(0.9\) grams/cubic centimeter. Consider the value of \( \pi = 3.14 \).
Shown below is an ice-cream cone completely filled with ice-cream. Assume the top portion (visible portion of ice-cream) is a perfect hemisphere. What is the total mass of the ice-cream in grams? The density of ice-cream is \(0.9\) grams/cubic centimeter. Consider the value of \( \pi = 3.14 \).
Show Hint
For composite solids:
\begin{itemize}
\item Break the object into standard shapes,
\item Calculate volumes separately,
\item Add volumes before applying density.
\end{itemize}
Updated On: Jan 30, 2026
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Solution and Explanation
Step 1: Identify the dimensions from the figure.
Diameter of hemisphere \(= 6\) cm
\[
\Rightarrow r = 3 \text{ cm}
\]
Height of cone \(= 9\) cm
\bigskip
Step 2: Volume of the hemisphere:
\[
V_{\text{hemisphere}} = \frac{2}{3}\pi r^3
= \frac{2}{3}\times 3.14 \times 3^3
= 56.52 \text{ cm}^3
\]
\bigskip
Step 3: Volume of the cone:
\[
V_{\text{cone}} = \frac{1}{3}\pi r^2 h
= \frac{1}{3}\times 3.14 \times 3^2 \times 9
= 84.78 \text{ cm}^3
\]
\bigskip
Step 4: Total volume of ice-cream:
\[
V_{\text{total}} = 56.52 + 84.78 = 141.3 \text{ cm}^3
\]
\bigskip
Step 5: Using density \(= 0.9\) g/cm\(^3\), mass of ice-cream:
\[
\text{Mass} = 0.9 \times 141.3 = 127.17 \text{ g}
\]
\bigskip
Final Answer:
\[
\boxed{126 \text{ g to } 128 \text{ g}}
\]
\bigskip
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