Chapter 4 Systems of Measurement and Conversions
Total surface area:
750 in2 + 1150 in2 + 690 in2 + 353.43 in2
+ 490.87 in2 = 3434.3 in2
Paint: convert to square feet using a scale factor
1 ft equals 12 in.
2
Area in sq ft: (3434.3 in2) 1 = 23.85 or 24 ft2
12
Two coats: 2 × 24 = 48 ft2
( )
She needs enough paint to cover 48 ft2, so she
needs one quart of paint, which costs $14.99.
Wood stain: convert to square metres.
Area in m2:
(48 ft2) 1 m 2 = 4.46 m2
3.2808 ft
(
)
She needs enough stain to cover 4.46 m2,
so she needs one litre of stain, which costs
$12.99.
The stain is the cheaper option.
4. The seed hopper is hollow and is composed of
one cylinder and two cones. Find the area of
the side of the cylinder and the side of 2 cones.
The formula for the area of the side of a
cylinder is 2 π rh.
Find the radius of the cylinder.
3.5 yd = 1.75
2
Substitute the known values into the formula.
A = 2πrh
A = 2 π (1.75) (4.7)
A = 51.68 yd2
245
sheet metal.
5. a) Convert the measurements from inches to
yards.
40″ × 1 yard = 1.11 yard
36 inches
32″ × 1 yard = 0.89 yard
36 inches
26″ × 1 yard = 0.72 yard
36 inches
Find surface area of pit in square yards.
Side walls: 0.89 yd × 0.72 yd × 2 = 1.28 yd2
Back wall: 1.11 yd × 0.72 y = 0.80 yd2
Floor: 0.89 yd × 1.11 yd = 0.99 yd2
1.28 + 0.80 + 0.99 = 3.07 yd2
Add 5%.
3.07 yd2 × 1.05 = 3.22 yd2
48 bricks
Multiply by   __________
    
   
. 
2
1 yd
3.22 yd2 × 48 bricks
= 154.56
1 yd2
Francine should buy 155 bricks.
b) Multiply the number of bricks by $0.80.
155 × $0.80 = $124.00
The bricks will cost $124.00.
6. Have students draw a geometric net of the box
and label the dimensions of the sides. Convert
1 yd by 1 yd to 36 in by 36 in.
36 in
The formula for the area of the side of a cone is
π rs.
Substitute the known values into the formula.
A = 2πrh
A = π (1.75) (2.73)
A = 15.01 yd2
Find the sum of the areas of the side of the
cylinder and the side of the two cones.
51.68 + 15.01 + 15.01 = 81.70
To build the hopper will require 81.70 yd2 of
36 in
36 in