Question 1: Calculate the volume of a prism with a cross-sectional area of 12 cm² and a length of 15 cm.

Answer: 180

Question 2: A rectangular prism has a cross-sectional area of 24 cm² and a length of 10 cm. What is its volume?

Answer: 240

Question 3: Construct a triangular cross-section with an area of 6 cm² and a length of 8 cm. Calculate the volume of the prism.

Answer: 48

Question 4: What is the volume of a prism with a regular hexagonal cross-section of area 18 cm² and a length of 20 cm?

Answer: 360

Question 5: A trapezoidal cross-section has an area of 9 cm². If the prism's length is 12 cm, what is its volume?

Answer: 108

Question 6: A cylinder with a circular cross-section of area 78.5 cm² and length 10 cm is formed. Find its volume.

Answer: 785

Question 7: Explain why a prism with a larger cross-sectional area but shorter length can have the same volume as one with a smaller cross-sectional area but longer length. Use an example with numbers.

Answer: Since volume = area × length, increasing the area while decreasing the length proportionally can result in the same volume.

Question 8: A prism's cross-sectional shape is a parallelogram with an area of 30 cm². If the length of the prism is 25 cm, what is its volume?

Answer: 750

Question 9: Identify and correct the mistake in this calculation: A prism with cross-sectional area 20 cm² and length 8 cm was calculated to have volume 100 cm³.

Answer: Incorrect; actual volume is 20×8=160 cm³. The error was in the calculation or assumption.

Question 10: Construct a prism with a cross-section that is a trapezium, with an area of 15 cm². If the length is 14 cm, compute its volume.

Answer: 210

Question 11: Plot the graph of y=2x for x from 0 to 10. How might this relate to understanding volumes where cross-sectional areas change linearly with position?

Answer: The area changes proportionally to x; integrating or summing these areas can help find total volume.