Unit 7 – MeasurementReview Sheet

Day 1: Metric and Imperial Measurements

  1. Make the following conversions accurate to two decimal places:
  2. 32.5 fl. oz.  quartse. 1112 cm²  in.²
  3. 55 kg  lbsf. 0.75 mi.²  km²
  4. 13.1 mi.  metresg. 9298 in.³  m³
  5. 11.2 tons  kilograms h. 159065 cm³  yd³

Day 2: Area & Perimeter of 2-D Objects

  1. Calculate the area AND perimeter of the following composite figures, to two decimal places:
  2. b.

Day 3: SA of 3-D Objects

  1. A propane truck, as seen below, has a tank made from hard alloy steel. Determine the surface area of the tank to the nearest tenth of a metre.

Day 4: Volume of 3-D Objects

  1. Determine how much water this swimming pool can hold if it is filled to 0.3m from the top, to the nearest tenth of a cubic metre.

Day 5: Properties of Circles

  1. Determine the sector area, arc length, and segment area in a circle with a radius of 12 cm and a central angle of 29°, to two decimal places.

Day 6: Investigating Properties of Circles

  1. Determine the values of each variable and justify your answers with the corresponding property from the notes.
  2. b.

Day 7: Applications of Circle Geometry

  1. Considering the diagram below of a drive belt stretched around three drive cylinders.
  2. Drive cylinder 1 has a radius of 3.7 cm and the belt contacts the cylinder over 130°.
  3. Drive cylinder 2 contacts the belt over 9.1 cm (which is a central angle of 108°).
  4. Drive cylinder 3 has a radius of 3.9 cm and the belt contacts the cylinder over 16.4 cm.
  1. Determine the distance over which the belt contacts cylinder 1.
  2. Determine the radius of cylinder 2.
  3. Determine the sector angle over which the belt contact cylinder

Answers:

  1. a.) 1.02 qtse.) 172.36 in²

b.) 121.25 lbsf.) 1.94 km²

c.) 21 082.41 mg.) 0.15 m³

d.) 10 160.47 kgh.) 0.21 yd³

  1. a.) Area = 51.77cm², Perimeter = 26.82cm

b.) Area = 108m², Perimeter = 64m

  1. SA = 37.7m²
  2. V = 92.5m³
  3. Arc Length = 6.07cm, Sector Area = 36.44cm², Segment Area = 1.54cm²
  4. a.) x = 5m (Prop. 6), y = 36º (Prop. 3), z = 2.4m (Prop. 5)

b.) x = 3cm (Prop. 2), y = 6cm (Prop. 1), a = 50º , b = 100º (Prop. 4)

  1. a.) Arc Length = 8.4cm

b.) Radius = 4.8cm

c.) Sector Angle = 240.9º