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 = 0.9 grams/cubic centimeter. Consider the value of $\pi$ = 3.14.
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Factorizing common terms like $\pi R^2$ first before inserting decimal values helps avoid arithmetic errors and speeds up computation during time-constrained exams.
Step 1: Find the two volumes. With $r=3$, $h=9$: cone $=\tfrac{1}{3}\pi r^2 h=\tfrac{1}{3}(3.14)(9)(9)=84.78$ cc and hemisphere $=\tfrac{2}{3}\pi r^3=\tfrac{2}{3}(3.14)(27)=56.52$ cc. Step 2: Convert to mass. Total $=141.3$ cc, so mass $=0.9\times141.3$. \[ \boxed{127.17 \text{ g}} \]
