Sydney scale diagram, scale factor question

Question

Sydney drew a scale diagram of a circular fire pit in the center of a circular patio with an actual circumference of 15 m. The circle containing the fire pit is a reduction of the circular patio, by a scale factor of 1/3. (Circumference = pi x diameter)

 

a.) Determine the diameter of the actual fire pit, to the nearest of a metre.

 

b.) What is the diameter of the fire pit in the scale diagram if the scale factor used was 2/15?

 

c.) After construction, the raised pit will have a surface area of 6.47 m². What will be the surface area of a similar fire pit that is enlarged by a scale factor of 3?

 

d.) After construction, the raised fire pit will have a volume of 0.99 m^3. If the volume of the enlargement is 26.73 m³, what scale factor was used?  

Answer 1

Hi Nimo,

 

Since the actual diameter of the fire pit is 15m and the formula for the circumference is C = πd, substitute the circumference of 15m into the formula and solve for d.   

                                               15 = πd    and then divide both sides by π getting  d = 15/π = 5 rounded to the nearest meter.  The scale drawing is smaller so    (2/15) times 5 is 10/15 or 2/3 m

 If the raised fire pit has a surface area of 6.47 and a similar one larger by a factor of 3 would have a surface area of 

                6.47 times 3 = 19.41 or 20m² rounded to the nearest square meter. 

 

 For the last part, if the volume of the fire pit is .99m³ and the enlargement is 26.73m³, the scale factor used is 

 

              .99x = 26.73     ror x = 27