Question 1: A cylinder has a radius of 3 cm and a height of 10 cm. Recall that the surface area (SA) of a cylinder is given by SA = 2πr(h + r).

Answer: 2π×3×(10+3)=2×3.14×3×13=2×3.14×3×13=244.68cm^2

Question 1: Calculate the volume of a cylinder with radius 4 cm and height 9 cm. Use V=πr^2h.

Answer: π×4^2×9=3.14×16×9=452.16cm^3

Question 2: A student mistakenly uses the formula SA=2πrh + 2πr^2 for the surface area of a cylinder. Identify the error and explain why it is incorrect.

Answer: The correct formula for surface area is 2πr(h + r). The student used 2πrh + 2πr^2, which is equivalent, so there is no error in this case. If they used only 2πrh, they would be missing the top and bottom circles.

Question 3: Construct a cylinder on the grid with radius 2 cm and height 5 cm.

Answer: Student draws a circle of radius 2 cm and extends vertically 5 cm.

Question 4: A cylinder’s surface area is calculated as 188.4 cm^2 with r=3 cm and h=5 cm. Check whether this calculation is correct.

Answer: SA=2πr(h+r)=2×3.14×3×(5+3)=2×3.14×3×8=150.72cm^2, so 188.4cm^2 is incorrect.

Question 1: A cylindrical water tank has a radius of 5 meters and a height of 12 meters. Calculate its volume. Then, determine how much water (in litres) it can hold, given that 1 m^3 = 1000 litres.

Answer: Volume=π×5^2×12=3.14×25×12=9420cm^3=9.42m^3; in litres=9.42×1000=9420 litres

Question 2: A cylinder with radius 7 cm is painted on its lateral surface. If the total paint area used is 440 cm^2, what is the height of the cylinder? Use the lateral surface area formula SA_lateral=2πrh.

Answer: 440=2×3.14×7×h; h=440/(2×3.14×7)=440/43.96≈10cm

Question 3: Explain why using the formula SA=2πr(h + r) might lead to errors if students forget to double the πr(h + r) term.

Answer: Because the formula for surface area of a cylinder is 2πr(h + r). Forgetting to double the entire expression results in only calculating one side, underestimating the surface area.

Question 1: A manufacturing factory produces cylindrical cans with radius 4 cm and height 10 cm. If each can is painted on the outside, how much paint area is needed per can? Use the lateral surface area formula.

Answer: SA_lateral=2πr h=2×3.14×4×10=251.2cm^2

Question 2: A water tank in the shape of a cylinder is designed to hold 10,000 litres of water. Determine the required radius if the height of the tank is 5 meters. (Use V=πr^2h and 1 m^3=1000 litres).

Answer: V=10,000/1000=10m^3; r=√(V/πh)=√(10/3.14×5)=√(10/15.7)=√0.637≈0.798m

Question 1: A cylinder has a volume of 1500 cm^3, and its height is twice its radius. Find the radius and height of the cylinder.

Answer: Let r be radius, h=2r; V=πr^2h=πr^2×2r=2πr^3=1500; r^3=1500/(2π)=1500/6.28≈238.92; r=∛238.92≈6.2cm; h=2×6.2=12.4cm

Question 2: A cylindrical tank with radius 3 meters is filled with water up to a height of 8 meters. Calculate the total surface area if the tank is to be painted on all sides including top and bottom, but excluding the water surface.

Answer: Surface area=2πr(h + r)=2×3.14×3×(8+3)=2×3.14×3×11=208.32m^2

Question 1: A student calculates the surface area of a cylinder as 300 cm^2 using the formula 2πrh. Identify the mistake and correct it.

Answer: The formula 2πrh only accounts for the lateral surface area, not the total surface area. Correct formula: 2πr(h + r).

Question 2: Construct a cylinder with a height of 9 cm and a radius that makes its volume 500 cm^3. Show your reasoning.

Answer: r=√(V/πh)=√(500/3.14×9)=√(500/28.26)=√17.69≈4.2cm