Worksheet: Surface Areas of Cones

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

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.

  • Acircumference =3,136𝜋cm, area =112𝜋cm
  • Bcircumference =112cm, area =3,136cm
  • Ccircumference =112𝜋cm, area =3,136𝜋cm
  • Dcircumference =3,136cm, area =112cm

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, is its total surface area?

  • A1,755𝜋
  • B1,026𝜋
  • C729𝜋
  • D695.25𝜋

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

  • A40510𝜋 cm2
  • B117𝜋 cm2
  • C4510𝜋 cm2
  • D1822𝜋 cm2

Q8:

Given that the height of the shown cone is 88 cm, and sin𝜃=35, determine the surface area of the cone in terms of 𝜋.

  • A8,664𝜋 cm2
  • B7,260𝜋 cm2
  • C4,356𝜋 cm2
  • D11,616𝜋 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 450𝜋 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 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?

  • A14
  • B14
  • C12
  • D4
  • E2

Q14:

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

  • A32𝜋𝑙
  • B𝜋𝑙
  • C3𝜋𝑙
  • D𝜋𝑙
  • E2𝜋𝑙

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 364𝜋 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?

  • A121256
  • B256121
  • C1611
  • D1116
  • E16121

Q21:

Given that the volume of a right-cone-shaped water tank is 15 m3 and that its height is 6.5 m, find its total surface area, approximating the result to the nearest hundredth.

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