# Worksheet: Lateral and Total Surface Areas of a Cone

Q1:

Determine, to the nearest hundredth, the total surface area of the cone shown.

Q2:

A right circular cone has base diameter 10 cm and height 12 cm. Determine the total surface area to the nearest tenth.

Q3:

A right circular cone has height 90 cm and slant height 106 cm. Find the circumference and area of the base in terms of .

• Acircumference , area
• Bcircumference , area
• Ccircumference , area
• Dcircumference , area

Q4:

The radius of the base of a right circular cone is 27 cm and its slant height is 38 cm. What, in terms of , is its total surface area?

• A
• B
• C
• D

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 its surface area to the nearest square centimetre.

Q7:

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

• A cm2
• B cm2
• C cm2
• D cm2

Q8:

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

• A cm2
• B cm2
• C cm2
• D cm2

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 cm2. What is the radius of its base?

Q11:

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

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 millimetres and 10 millimetres. What is the ratio of the surface area of the small cone to the surface area of the large one?

• A
• B4
• C2
• D

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 coneβs 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 centimetre, the surface area of a right cone whose slant height is 73 cm and height is 61 cm.

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 cm2 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 43.96 cm
• C 33.04 cm
• D cm

Q22:

Karim 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?

• A67.5
• B155.88
• C
• D

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 cm3 and that the length of is cm, determine its total surface area in terms of .

• A cm2
• B cm2
• C cm2
• D cm2