Calculating a pyramid

Calculating a pyramid

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This task is about working out the surface area and volume of a pyramid.

Area of triangle = 1/2 base × height
Volume of a pyramid = 1/3 area of base × height
An architect designed this modern pyramid building which is 24 metres tall.
It has a square base with each side of the base being 14 metres long.
 
a)
Calculate the total area of the four outside faces of the pyramid.
Please show your working.   
 

 

 

 

Total area of the outside faces = __________ m2

 
b) i)
Calculate the volume of the pyramid.
 
 
 
 

Volume of the pyramid = __________ m3

 
  ii)
Regulations state that each person in the pyramid needs 8 m3 of airspace.
If the walls take up 48 m3, calculate the greatest number of people allowed inside the pyramid?

 

 

 


Maximum number of people = __________
Level:
5
Curriculum info: 
Maths, Geometry and Measurement, Measurement
Keywords: 
area, volume, triangles, 3-dimensional shapes
Description of task: 
Students calculate the surface area and volume of a pyramid.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Measurement sense, sets 7-8
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y10 (08/2000)

a)

  

700
 
Any 1 of:

  • Calculates area of a triangle as 1/2 b × h but uses wrong dimensions.
  • 175 (calculates for one face only)
  • 896 (includes area of base)

difficult
 
moderate

b)

i)
ii)

1568
190 [accept (answer to b)i) - 48) ¸ 8]

difficult
difficult
Diagnostic and formative information: 
 

Common error

Likely calculation

Likely reason

a)

672

168

( 1⁄2 × 14 × 24) × 4

(1⁄2 × 14 × 24)
  • Reads height of a face as 24 m rather than 25 m.
  • As above, but calculates for 1 face only.

b)

1633.3

1⁄3 ´ 14 × 14 × 25

Reads height of pyramid as 25 m rather than 24 m.