Question 1: Calculate the surface area of a cone with a radius of 3 cm and a slant height of 5 cm using the formula πr² + πrl. Use π ≈ 3.14.

Answer: Calculate: π×3² + π×3×5 = 3.14×9 + 3.14×15 = 28.26 + 47.1 = 75.36

Question 2: A cone has a radius of 4 meters and a slant height of 6 meters. Find its surface area, approximating π as 3.14.

Answer: Calculate: 3.14×4² + 3.14×4×6 = 3.14×16 + 3.14×24 = 50.24 + 75.36 = 125.6

Question 3: If a cone's radius is 5 cm and its lateral slant height is 8 cm, what is its surface area? Show your working.

Answer: Calculate: 3.14×5² + 3.14×5×8 = 3.14×25 + 3.14×40 = 78.5 + 125.6 = 204.1

Question 4: Construct a cone on the grid with a radius of 2 units and a slant height of 4 units. Then, calculate its surface area.

Answer: Calculate: 3.14×2² + 3.14×2×4 = 3.14×4 + 3.14×8 = 12.56 + 25.12 = 37.68

Question 5: Plot the graph of y=2x for x values from 0 to 5 on the grid.

Answer: Students plot points (0,0), (1,2), (2,4), (3,6), (4,8), (5,10).

Question 6: Construct a triangle with sides of 3, 4, and 5 units. Use the grid to draw the triangle accurately.

Answer: Students draw the triangle; then, calculate the surface area of a cone with those dimensions if applicable.

Question 7: A cone has a radius of 6 cm and a slant height of 10 cm. What is its surface area? Approximate π as 3.14.

Answer: Calculate: 3.14×6² + 3.14×6×10 = 3.14×36 + 3.14×60 = 113.04 + 188.4 = 301.44

Question 8: A real-world scenario: A company is designing a conical party hat with a radius of 7 inches and a slant height of 9 inches. Find the surface area for material estimation.

Answer: Calculate: 3.14×7² + 3.14×7×9 = 3.14×49 + 3.14×63 = 153.86 + 197.82 = 351.68

Question 9: Identify and correct the mistake in this calculation: Surface area = 3.14×5 + 3.14×5×7 = 15.7 + 109.9 = 125.6.

Answer: Mistake: The formula should be πr² + πrl, so 3.14×5² + 3.14×5×7 = 3.14×25 + 3.14×35 = 78.5 + 109.9 = 188.4. The original calculation used r instead of r² in the first term.

Question 10: A cone's radius is doubled from 3 cm to 6 cm, and the slant height remains 5 cm. How does the surface area change? Show your reasoning.

Answer: Original: 3.14×3² + 3.14×3×5 = 28.26. New: 3.14×6² + 3.14×6×5 = 113.04 + 94.2 = 207.24. Change: surface area increases by 178.98 cm².