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Lesson: Lateral and Total Surface Areas of a Cone

Sample Question Videos

Worksheet • 25 Questions • 4 Videos

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 πœ‹ .

  • Acircumference = 1 1 2 πœ‹ c m , area = 3 1 3 6 πœ‹ c m 2
  • Bcircumference = 3 1 3 6 πœ‹ c m , area = 1 1 2 πœ‹ c m 2
  • Ccircumference = 3 1 3 6 c m , area = 1 1 2 c m 2
  • Dcircumference = 1 1 2 c m , area = 3 1 3 6 c m 2

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 πœ‹ , is its total surface area?

  • A 1 7 5 5 πœ‹
  • B 1 0 2 6 πœ‹
  • C 6 9 5 . 2 5 πœ‹
  • D 7 2 9 πœ‹

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 πœ‹ , the lateral area of a right cone with base radius 9 cm and height 13 cm.

  • A 4 5 √ 1 0 πœ‹ cm2
  • B 4 0 5 √ 1 0 πœ‹ cm2
  • C 1 1 7 πœ‹ cm2
  • D 1 8 √ 2 2 πœ‹ cm2

Q8:

Given that the height of the shown cone is 88 cm, and s i n πœƒ = 3 5 , determine the surface area of the cone in terms of πœ‹ .

  • A 1 1 6 1 6 πœ‹ cm2
  • B 7 2 6 0 πœ‹ cm2
  • C 8 6 6 4 πœ‹ cm2
  • D 4 3 5 6 πœ‹ 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 4 5 0 πœ‹ 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:

𝐴 𝐡 𝐢 is an equilateral triangle of side length 𝑙 . Given that it turned one complete revolution about 𝐡 𝐢 , determine the lateral area of the solid generated by the rotation in terms of πœ‹ and 𝑙 .

  • A √ 3 πœ‹ 𝑙 2
  • B 2 πœ‹ 𝑙
  • C √ 3 2 πœ‹ 𝑙 2
  • D πœ‹ 𝑙
  • E πœ‹ 𝑙 2

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 2 7 5 ∘ is folded in a way so that the points 𝐴 and 𝐡 meet to form a circular cone of the greatest possible area. Determine the cone’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 3 6 4 πœ‹ 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 2 0 3 πœ‹ cm2 is folded into a right cone, by gluing together the radii 𝐴 𝐡 and 𝐴 𝐢 . 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 6 √ 2 2 cm
  • B 43.96 cm
  • C 33.04 cm
  • D √ 8 9 0 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 1 2 0 ∘ is folded into a right circular cone. What is the height of this cone?

  • A 9 0 √ 2
  • B155.88
  • C 3 √ 1 0
  • D67.5

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 1 6 1 1
  • B 1 6 1 2 1
  • C 1 1 1 6
  • D 1 2 1 2 5 6
  • E 2 5 6 1 2 1

Q25:

Given that the following net describes a solid of volume 2 0 , 4 8 0 πœ‹ cm3 and that the length of 𝐡 𝐢 is 6 4 πœ‹ cm, determine its total surface area in terms of πœ‹ .

  • A 3 , 2 0 0 πœ‹ cm2
  • B 2 , 1 7 6 πœ‹ cm2
  • C 1 , 9 2 0 πœ‹ cm2
  • D 2 , 9 4 4 πœ‹ cm2
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