# Worksheet: Lateral and Total Surface Areas of a Cone

In this lesson, we will practice finding the lateral and total surface areas of a cone using the formula.

**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
- B2
- C
- D4
- E

**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 piece of paper in the shape of a circular sector having a radius of 72 cm and an angle of is folded in a way so that the points and meet to form a circular cone of the greatest possible area. Determine the coneβs height to the nearest hundredth.

**Q18: **

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.

**Q19: **

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

- A
4,294 cm
^{2} - B
4,132 cm
^{2} - C
5,654 cm
^{2} - D
6,221 cm
^{2}

**Q20: **

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.

**Q21: **

A sheet of paper in the shape of a sector of radius 29 cm
and area cm^{2} is folded into a right cone, by
gluing together the radii and .
What is the height of the cone? Recall that the sector area is given by half the product of
its radius and the length of its arc.

- A cm
- B cm
- C 33.04 cm
- D 43.96 cm

**Q22: **

David cuts a slit in a circular piece of paper and then rolls it into a cone so that the sides of the cone are two sheets thick. What is the apex angle of the cone?

**Q23: **

A circular sector of radius 135 and angle is folded into a right circular cone. What is the height of this cone?

- A
- B67.5
- C
- D155.88

**Q24: **

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

**Q25: **

Given that the following net describes a solid of volume cm^{3} and that the length of is cm, determine its total surface area in terms of .

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