From the given descriptions and dimensions, we have;
6. 2000 cm²
7. 81 m²
8. a. 138 m²
b. 538 m²
c. 62 cm²
9. $107.25
Which method can be used to calculate the surface areas and cost?
6. Type of box = Open box with no lid
Side length of the box = 20 cm
Therefore;
Number of faces of the box, painted = 5
Area of a face of the box = 20² = 400
- Area of the surface painted, A = 5 × 400 cm² = 2000 cm²
7. Area of the plastic to cover one book, A, is found as follows;
A = 2 × 20 × 15 + 2 × 3 × 15 + 2 × 20 × 3
Which gives;
The area of plastic needed to cover 1000 books is therefore;
Total area = 1,000 × 810 cm² = 810,000 cm²
Conversion of cm² to m² gives;
Therefore;
A = 810,000 cm² = 810,000 cm² × 1/10,000 m²/cm² = 81 m²
- The area of plastic needed to cover 1000 books is A = 81 m²
8. The surface areas are;
a. A = 2 × 3 × 6 + 5 × 6 + 7 × 6 + 2×3×(3+7)/2 = 138
- The surface area is 138 m²
b. A = 2 × 15 × 5 + 2×(10×5 + (6×8)/2) + 2×8×15 = 538
A = 150 + 148 + 240 = 538
- The surface area is 538 m²
c. From the congruent marks, we have;
A = 5 × 3 × 3 + 5×1×3 + 2×1×1 = 62
- The surface area is 62 cm²
9. From the congruent markings, we have;
A = 2 × (1.5 × 1.5 + (1.5 × 1.3)/2) + 5×2×1.5
A = 6.45 + 15 = 21.45
Surface area of a the canvas, A = 21.45 m²
Cost per unit area of the canvas, c = $5
Cost of the canvas for the tent, C, is therefore;
- C = $5/m² × 21.45 m² = $107.25
Learn more about the finding the surface area of solids here:
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