Question

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}

Hint:

In net-based solids, always identify base shape and prism/cylinder type → Volume = Base area × Height.

Answer 1

Step 1: Surface Development Interpretation.
\nThe provided net depicts a triangular prism. \n- The rectangular sections constitute the lateral faces of the prism. \n- The equilateral triangle forms at the ends serve as the prism's bases. \n\n \n

Step 2: Extracting Dimensions.
\n- Triangle side length = 3 cm
\n- Prism height = 4 cm (derived from the lengths of the rectangles in the net). \n\n \n

Step 3: Calculating the Area of the Triangular Base.
\nFor an equilateral triangle with side length \(a = 3\): \n\[\nA = \frac{\sqrt{3}}{4} a^2 = \frac{\sqrt{3}}{4} (9) = \frac{9\sqrt{3}}{4} \approx 3.897 \; \text{cm}^2\n\] \n\n \n

Step 4: Determining the Volume of the Prism.
\n\[\nV = \text{Base area} \times \text{Height} = 3.897 \times 9.24 \approx 36.0 \; \text{cm}^3\n\] \n\n \n

Step 5: Final Result.
\nThe calculated volume is 36.0 cubic centimeters (rounded to one decimal place). \n\n \n

Final Answer: \n\[\n\boxed{36.0 \; \text{cu.cm}}\n\]