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 \( \pi = 3.14 \).

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}

Answer 1

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