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Area, SMB-036

Find the surface area of the solid pictured below which is composed of a right cone with a hemisphere attached to the base. Give your answer to the nearest square centimetre.  (3 marks)
  

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\(\ 616\ \text{cm}^2\)

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\(\text{SA (hemisphere)}\) \(= \dfrac{1}{2} \times 4 \pi r^2\)  
  \(= \dfrac{1}{2} \times 4 \pi \times 7^2\)  
  \(=307.87…\ \text{cm}^2\)  

 

\(\text{SA (cone)}\) \(= \pi rl\)  
  \(= \pi \times 7 \times 14\)  
  \(=307.87…\ \text{cm}^2\)  

 
\(\text{Total SA}\ = 2 \times 307.87… = 616\ \text{cm}^2\ \ (\text{nearest cm}^2) \)

Area, SMB-018

A right cone with perpendicular height of 8 cm, slant height of 10 cm and a base diameter of 12 cm is pictured below.
 

Find the total surface area of the cone, including its base, correct to two decimal places.   (3 marks)

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\(301.59\ \text{cm}^2 \)

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\(r = 6\ \text{cm}, \ l =  10\ \text{cm} \)

\(\text{SA}\) \(= \pi r^2 + \pi r l\)  
  \(=  \pi \times 6^2 + \pi \times 6 \times 10 \)  
  \(=301.592… \)  
  \(=301.59\ \text{cm}^2\ \text{(2 d.p.)}\)  

Area, SMB-017

A square pyramid with a slant height of 15 centimetres is pictured below.
 

Find the total surface area of the pyramid, including its base.   (2 marks)

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\(400\ \text{cm}^2 \)

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\(\text{SA}\) \(= (10 \times 10) + 4 \times (\dfrac{1}{2} \times 10 \times 15)\)  
  \(=100 + 4(75) \)  
  \(=400\ \text{cm}^2 \)  

Area, SMB-016

A square pyramid with a perpendicular height of 8 metres is pictured below.
 

  1. Using Pythagoras, calculate the slant height of the pyramid.   (2 marks)
  1. Find the total surface area of the pyramid, including its base, to the nearest square metre.   (2 marks)
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i.    \(10\ \text{m} \)

ii.    \(384\ \text{m}^2 \)

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i.    \(\text{Let}\ \ s =\ \text{slant height}\)

\(s^2\) \(=6^2 + 8^2\)  
  \(=100\)  
\(s\) \(=10\ \text{m}\)  

 

ii.    \(\text{SA}\) \(= (12 \times 12) + 4 \times (\dfrac{1}{2} \times 12 \times 10)\)  
  \(=144 + 4(60) \)  
  \(=384\ \text{m}^2 \)  

Area, SMB-030

A glass aviary is made up of four triangles and a square, as shown in the diagram below.

Harry is hired to clean the interior sides of the aviary, not including the floor.

What is the area that Harry will need to clean?   (2 marks)

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`402\ text(m)^2`

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`text(Area to clean)`

`= 4 xx 1/2 bh`

`= 4 xx 1/2 xx 15 xx 13.4`

`= 402\ text(m)^2`