Surface Area worksheet

1. Total surface area: 50.27 mm²

1. A sphere's surface equals four circles of the same radius: 4 × π × r²

   $4\times \pi \times 2^2$$=50.265482\text{\hspace{0.17em}mm²}$

2. To convert to square meters, multiply by (1 mm in meters)²

   $50.265482\text{\hspace{0.17em}mm²}\times {0.001}^2$$=0.00005\text{\hspace{0.17em}m²}$

2. Total surface area: 40.72 ft²

1. A sphere's surface equals four circles of the same radius: 4 × π × r²

   $4\times \pi \times {1.8}^2$$=40.715041\text{\hspace{0.17em}ft²}$

2. To convert to square meters, multiply by (1 ft in meters)²

   $40.715041\text{\hspace{0.17em}ft²}\times {0.3048}^2$$=3.782551\text{\hspace{0.17em}m²}$

3. Total surface area: 42 m²

1. A box has three pairs of matching rectangles, so add one of each and double it

   $2\times \left(3\times 3+3\times 2+3\times 2\right)$$=2\times \left(9+6+6\right)$$=42\text{\hspace{0.17em}m²}$

4. Total surface area: 54 cm²

1. A cube has six matching square faces, so multiply the area of one face (edge²) by 6

   $6\times 3^2$$=54\text{\hspace{0.17em}cm²}$

2. To convert to square meters, multiply by (1 cm in meters)²

   $54\text{\hspace{0.17em}cm²}\times {0.01}^2$$=0.0054\text{\hspace{0.17em}m²}$

5. Total surface area: 25.39 m²

1. Find the slant height (l), the length along the sloping side, with the Pythagorean theorem

   $l$$=\sqrt{{1.8}^2+2^2}$$=2.690725$

2. Curved surface: π times the radius times the slant height

   $\pi \times 1.8\times 2.690725$$=15.21569\text{\hspace{0.17em}m²}$

3. Circular base: π times the radius squared

   $\pi \times {1.8}^2$$=10.17876\text{\hspace{0.17em}m²}$

4. Total: curved surface plus base

   $15.21569+10.17876$$=25.394451\text{\hspace{0.17em}m²}$

6. Total surface area: 42 ft²

1. A box has three pairs of matching rectangles, so add one of each and double it

   $2\times \left(3\times 3+3\times 2+3\times 2\right)$$=2\times \left(9+6+6\right)$$=42\text{\hspace{0.17em}ft²}$

2. To convert to square meters, multiply by (1 ft in meters)²

   $42\text{\hspace{0.17em}ft²}\times {0.3048}^2$$=3.901928\text{\hspace{0.17em}m²}$

7. Total surface area: 50.85 yd²

1. Find the slant height of the two faces on the length edges, using the height and half the width

   $\sqrt{3^2+{\left(\frac{3}{2}\right)}^2}$$=3.354102$

2. Find the slant height of the two faces on the width edges, using the height and half the length

   $\sqrt{3^2+{\left(\frac{6}{2}\right)}^2}$$=4.242641$

3. Add the four triangles, in two pairs. Each triangle is half its base edge times its slant height

   $6\times 3.354102+3\times 4.242641$$=32.852534\text{\hspace{0.17em}yd²}$

4. Total: the triangular faces plus the rectangular base (l × w)

   $32.852534+6\times 3$$=50.852534\text{\hspace{0.17em}yd²}$

5. To convert to square meters, multiply by (1 yd in meters)²

   $50.852534\text{\hspace{0.17em}yd²}\times {0.9144}^2$$=42.519195\text{\hspace{0.17em}m²}$

8. Total surface area: 48 ft²

1. A box has three pairs of matching rectangles, so add one of each and double it

   $2\times \left(5\times 2+5\times 2+2\times 2\right)$$=2\times \left(10+10+4\right)$$=48\text{\hspace{0.17em}ft²}$

2. To convert to square meters, multiply by (1 ft in meters)²

   $48\text{\hspace{0.17em}ft²}\times {0.3048}^2$$=4.459346\text{\hspace{0.17em}m²}$

9. Total surface area: 11.69 yd²

1. Find the slant height (l), the length along the sloping side, with the Pythagorean theorem

   $l$$=\sqrt{{1.1}^2+2^2}$$=2.282542$

2. Curved surface: π times the radius times the slant height

   $\pi \times 1.1\times 2.282542$$=7.8879\text{\hspace{0.17em}yd²}$

3. Circular base: π times the radius squared

   $\pi \times {1.1}^2$$=3.801327\text{\hspace{0.17em}yd²}$

4. Total: curved surface plus base

   $7.8879+3.801327$$=11.689228\text{\hspace{0.17em}yd²}$

5. To convert to square meters, multiply by (1 yd in meters)²

   $11.689228\text{\hspace{0.17em}yd²}\times {0.9144}^2$$=9.773683\text{\hspace{0.17em}m²}$

10. Total surface area: 6 mm²

1. A cube has six matching square faces, so multiply the area of one face (edge²) by 6

   $6\times 1^2$$=6\text{\hspace{0.17em}mm²}$

2. To convert to square meters, multiply by (1 mm in meters)²

   $6\text{\hspace{0.17em}mm²}\times {0.001}^2$$=0.000006\text{\hspace{0.17em}m²}$