The surface development of a three dimensional object is shown in the figure. The dotted lines indicate the folds. The dimensions given in the figure are in cm. The volume of the three-dimensional object (in cu.cm) is \underline{\hspace{1cm}} [rounded off to one decimal place].
\begin{center}
\includegraphics[width=0.5\textwidth]{07.jpeg}
\end{center}
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Solution and Explanation
Step 1: Interpret the surface development.
The given net represents a triangular prism.
- The rectangle strips form the prism's lateral faces.
- The equilateral triangle shapes at the ends form the prism's bases.
Step 2: Dimensions from figure.
- Triangle side = 3 cm
- Height of prism = 4 cm (from rectangle lengths in the net).
Step 3: Area of triangular base.
For equilateral triangle of side \(a = 3\):
\[
A = \frac{\sqrt{3}}{4} a^2 = \frac{\sqrt{3}}{4} (9) = \frac{9\sqrt{3}}{4} \approx 3.897 \; \text{cm}^2
\]
Step 4: Volume of prism.
\[
V = \text{Base area} \times \text{Height} = 3.897 \times 9.24 \approx 36.0 \; \text{cm}^3
\]
Step 5: Conclusion.
The volume = 36.0 cu.cm (rounded to one decimal).
Final Answer: \[ \boxed{36.0 \; \text{cu.cm}} \]
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