Question 1: Calculate the volume of a cone with radius 3 cm and height 8 cm.

Answer: 72π cm³

Question 2: Find the lateral surface area of a cone with slant height 10 cm and radius 4 cm. Use π ≈ 3.14.

Answer: 50.24 cm²

Question 3: A cone has a height of 12 cm and a base radius of 5 cm. What is its total surface area? (Use π ≈ 3.14)

Answer: 157.0 cm²

Question 4: A cone’s slant height is 15 cm, and the radius is 6 cm. Calculate its lateral surface area.

Answer: 180.96 cm²

Question 1: A conical paperweight has a radius of 4 cm and height of 9 cm. It is then reshaped so that its height doubles while the radius remains unchanged. What is the new volume? Explain your steps.

Answer: The original volume is (1/3)π(4)^2(9)=48π cm³. Doubling height to 18 cm gives a new volume of (1/3)π(4)^2(18)=96π cm³.

Question 2: A cone with a volume of 50π cm³ has a height of 10 cm. Find its radius. Show all working.

Answer: r = √( (3×50π)/ (π×10) ) = √15 ≈ 3.87 cm

Question 3: The slant height of a cone is mistakenly taken as the height in a calculation. How does this error affect the surface area calculation? Explain.

Answer: Using slant height as height overestimates the lateral area because the slant height is longer than the true height, leading to an over-calculation of surface area.

Question 1: A funnel is shaped like a cone with a radius of 5 cm and height of 10 cm. How much liquid (in cm³) can it hold if filled to the top? Calculate the volume.

Answer: ≈261.8 cm³

Question 2: An artist creates a conical sculpture with a radius of 15 inches and height of 40 inches. What is the approximate surface area needed to cover the sculpture? (Use π ≈ 3.14).

Answer: ≈3104.4 inches²

Question 1: A cone has a volume of 1000 cm³ and a slant height of 20 cm. Find its radius and height, showing all steps.

Answer: r ≈ 6.37 cm, h ≈ 8.5 cm

Question 2: A student incorrectly applies the surface area formula using the diameter instead of the radius in a cone. Identify the mistake and correct the calculation.

Answer: Mistake: Using diameter instead of radius doubles the actual radius, leading to overestimation. Correct by halving the diameter to get radius before calculating surface area.

Question 1: A student claims that the surface area of a cone is given by 2πrh + πr². Is this correct? If not, what is the correct formula?

Answer: Incorrect. Correct formula: πr(l + r), where l is the slant height.

Question 2: A cone’s volume is underestimated because the height is confused with the slant height. Explain the mistake and how to avoid it.

Answer: Mistake: Using slant height as height reduces the calculated volume. To avoid this, distinguish between slant height and vertical height and use the correct measurement in volume formula.