# Worksheet: Surface Areas of Cones

In this worksheet, we will practice calculating the lateral and total surface areas of cones using their formulas.

**Q5: **

Find, to the nearest hundredth, the total surface area of the given cone.

**Q6: **

A conical lampshade is 31 cm high and has a base of circumference 145.2 cm. Find the curved surface area of the outside of the lampshade. Give your answer to the nearest square centimeter.

**Q7: **

Find, in terms of , the lateral area of a right cone with base radius 9 cm and height 13 cm.

- A cm
^{2} - B cm
^{2} - C cm
^{2} - D cm
^{2}

**Q8: **

Given that the height of the shown cone is 88 cm, and , determine the surface area of the cone in terms of .

- A cm
^{2} - B cm
^{2} - C cm
^{2} - D cm
^{2}

**Q9: **

Find the total surface area of the right cone approximated to the nearest two decimal places.

**Q10: **

A right cone has slant height 35 cm
and surface area cm^{2}.
What is the radius of its base?

**Q11: **

Find, to the nearest tenth, the lateral area of a cone with a diameter of 40 centimeters and a slant height of 29 centimeters.

**Q12: **

Find, to the nearest tenth, the surface area of a cone with an altitude of 76 feet and a slant height of 95 feet.

**Q13: **

Two similar cones have radii of 5 millimeters and 10 millimeters. What is the ratio of the surface area of the small cone to the surface area of the large one?

- A
- B
- C
- D4
- E2

**Q14: **

is an equilateral triangle of side length . Given that it turned one complete revolution about , determine the lateral area of the solid generated by the rotation in terms of and .

- A
- B
- C
- D
- E

**Q15: **

Find the surface area of the given cone to the nearest tenth.

**Q16: **

Find, to the nearest tenth, the surface area of this cone.

**Q17: **

A conical mountain has a radius of 1.5 km and a perpendicular height of 0.5 km. Determine the lateral area of the mountain to one decimal place.

**Q18: **

Determine, to the nearest square centimeter, the surface area of a right cone whose slant height is 51 cm and height is 44 cm.

**Q19: **

The surface area of a cone is square inches, and the radius of the base is 13 inches. Determine the slant height of the cone.

**Q20: **

Two similar cones have surface areas of 768 and 363. What is the ratio of the height of the larger cone to that of the smaller one?

- A
- B
- C
- D
- E

**Q21: **

Given that the volume of a right-cone-shaped water tank is 15 m^{3} and that its height is 6.5 m, find its total surface area, approximating the result to the nearest hundredth.