Volume and Surface Area of Cones

Volume and Surface Area of Cones

Read each question carefully and show all your work. Use π ≈ 3.14 where necessary. Round your answers to two decimal places.

1. A conical party hat has a radius of 4 cm and a height of 9 cm. Calculate the volume of air inside the hat.

2. A pile of sand is in the shape of a cone with a diameter of 10 meters and a height of 7 meters. What is the volume of the sand pile?

3. An ice cream cone has a radius of 3 cm and a slant height of 8 cm. Calculate the lateral surface area of the cone (the part that holds the ice cream).

4. A traffic cone has a base radius of 15 cm and a height of 40 cm. Find the total surface area of the cone (exclude the bottom base as it sits on the ground).

5. Which of the following formulas represents the volume of a cone?

6. The lateral surface area of a cone is given by the formula:

7. The slant height of a cone can be found using the Pythagorean theorem if the radius and   are known.

8. The total surface area of a cone is the sum of its lateral surface area and the area of its  .

9. A cylindrical container with a radius of 5 cm and a height of 12 cm is filled with water. If this water is poured into a conical container with the same radius, what would be the height of the water in the conical container?