Measures and solids · Ages 14–15

Surface area of pyramids and cones worksheet

Part of: Cones & spheres

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Measures and solids · Ages 14–15

Numsprite
numsprite.com

Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The pyramid in the picture stands on a square of side 40 cm, and its four side faces each have a slant height of 29 cm. What is its total surface area, in cm²?
Answer:
2.The cone in the picture has a base radius of 16 cm and a slant height of 34 cm. What is its curved surface area, in terms of π?
Answer:
3.Taking π as 3.14, a cone has a base radius of 9 cm and a slant height of 29 cm. What is its curved surface area, in cm²?
Answer:
4.The solid cone in the picture has a base radius of 9 cm and a height of 12 cm. What is its total surface area, in terms of π?
Answer:
5.The solid cone in the picture has a base radius of 14 cm and a height of 48 cm. What is its total surface area, in terms of π?
Answer:
6.Taking π as 3.14, a cone has a base radius of 2 cm and a slant height of 6 cm. What is its curved surface area, in cm²?
Answer:
7.A cone has a base radius of 13 cm and a slant height of 15 cm. Cut its curved surface along a slanting line and lay it flat: it is a sector. What is the sector's angle at the centre, in degrees?
Answer:
8.The cone in the picture has a base radius of 45 cm and a curved surface area of 2295π cm². How high is it, in cm?
Answer:
9.The cone in the picture has a base radius of 5 cm and a curved surface area of 65π cm². How high is it, in cm?
Answer:

10.The solid cone in the picture has a base radius of 3 cm, a height of 4 cm and a slant height of 5 cm. What is its total surface area?
- A. 21π cm²
- B. 15π cm²
- C. 33π cm²
- D. 24π cm²
Choose the right answer
Answer:
11.The solid cone in the picture has a base radius of 24 cm, a height of 45 cm and a slant height of 51 cm. What is its total surface area?
- A. 1224π cm²
- B. 1800π cm²
- C. 1656π cm²
- D. 2376π cm²
Choose the right answer
Answer:
12.A cone of base radius 20 cm and height 21 cm has a curved surface area of 420π cm².
True or false?
Answer:

13.A cone-shaped party hat (no base) is 8 cm in radius and 15 cm high. Its slant height is cm, and it takes π cm² of paper.
Fill in each blank
Working:
Answer:
14.A roof is a pyramid on a square (no base), each base side 20 m, each triangle's slant height 26 m. Tiling costs $120 a square metre. How much does it cost in all, in dollars?
Working:
Answer:
15.A cone-shaped tent with a groundsheet is 6 m in radius with a slant height of 10 m. Its curved canvas takes π m², and with the groundsheet π m² in all; taking π as 3.14, m².
Fill in each blank
Working:
Answer:
16.A sector of cloth of radius 27 cm and angle 240° is curled into a cone-shaped lampshade, its two radii just meeting. What is the radius of the lampshade's base, in cm?
Working:
Answer:
17.A cone-shaped tent with a groundsheet is 7 m in radius with a slant height of 25 m. Its curved canvas takes π m², and with the groundsheet π m² in all; taking π as 3.14, m².
Fill in each blank
Working:
Answer:
18.A sector of cloth of radius 32 cm and angle 270° is curled into a cone-shaped lampshade, its two radii just meeting. What is the radius of the lampshade's base, in cm?
Working:
Answer:

Show the answers and working

Surface area of pyramids and cones worksheet: Answers and working

1. 3920 cm²
Each triangle is 40 × 29 ÷ 2 = 580, four of them 2320; the base 40² = 1600; 3920 cm² in all.
2. 544 π cm²
Curved surface = πrl = π × 16 × 34 = 544π cm².
3. 819.54 cm²
πrl = 3.14 × 9 × 29 = 819.54 cm².
4. 216 π cm²
Slant l = 9² + 12² = 15; πr² + πrl = π × 9² + π × 9 × 15 = 216π cm².
5. 896 π cm²
Slant l = 14² + 48² = 50; πr² + πrl = π × 14² + π × 14 × 50 = 896π cm².
6. 37.68 cm²
πrl = 3.14 × 2 × 6 = 37.68 cm².
7. 312°
The sector's radius is the slant 15, its arc the base's circumference 2π × 13: θ360 × 2π × 15 = 2π × 13, so θ = 360 × 13 ÷ 15 = 312°.
8. 24 cm
π × 45 × l = 2295π, so the slant l = 51; height = 51² − 45² = 24 cm.
9. 12 cm
π × 5 × l = 65π, so the slant l = 13; height = 13² − 5² = 12 cm.

10. D. 24π cm²
πr² + πrl = π × 3² + π × 3 × 5 = 24π cm².
11. B. 1800π cm²
πr² + πrl = π × 24² + π × 24 × 51 = 1800π cm².
12. False
The curved surface uses the slant: l = 20² + 21² = 29, so πrl = 580π cm².

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 17, 136
Slant 8² + 15² = 17; the curved surface only: π × 8 × 17 = 136π.
14. 124800 dollars
Four triangles 4 × 20 × 26 ÷ 2 = 1040 m², × $120 = $124,800.
15. 60, 96, 301.44
π × 6 × 10 = 60π; plus the groundsheet π × 6²: 96π; × 3.14 = 301.44.
16. 18 cm
The sector's arc becomes the base's circumference: 240360 × 2π × 27 = 2πr, so r = 27 × 240 ÷ 360 = 18 cm.
17. 175, 224, 703.36
π × 7 × 25 = 175π; plus the groundsheet π × 7²: 224π; × 3.14 = 703.36.
18. 24 cm
The sector's arc becomes the base's circumference: 270360 × 2π × 32 = 2πr, so r = 32 × 270 ÷ 360 = 24 cm.

Numsprite · numsprite.com/en/worksheets/cones-and-spheres/surface-area-of-pyramids-and-cones