Cake Servings worksheet

1. Servings: 97

1. Area of one slice on top of the cake: 1.5 × 2 in

   $1.5\times 2$$=3\text{\hspace{0.17em}in²}$

2. Tier 1 (13 in): find the area of the top, since every slice uses its own patch of it

   ${13}^2$$=169\text{\hspace{0.17em}in²}$

3. Tier 1 (13 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{169}{3}$$=56.33$$=56\text{\hspace{0.17em}servings}$

4. Tier 2 (10 in): find the area of the top, since every slice uses its own patch of it

   ${10}^2$$=100\text{\hspace{0.17em}in²}$

5. Tier 2 (10 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{100}{3}$$=33.33$$=33\text{\hspace{0.17em}servings}$

6. Tier 3 (5 in): find the area of the top, since every slice uses its own patch of it

   $5^2$$=25\text{\hspace{0.17em}in²}$

7. Tier 3 (5 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{25}{3}$$=8.33$$=8\text{\hspace{0.17em}servings}$

8. Add up the servings from every tier

   $56+33+8$$=97\text{\hspace{0.17em}servings}$

2. Servings: 67

1. Area of one slice on top of the cake: 1 × 2 in

   $1\times 2$$=2\text{\hspace{0.17em}in²}$

2. Tier 1 (10 in): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{10}{2}\right)}^2$$=78.54\text{\hspace{0.17em}in²}$

3. Tier 1 (10 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{78.54}{2}$$=39.27$$=39\text{\hspace{0.17em}servings}$

4. Tier 2 (7 in): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{7}{2}\right)}^2$$=38.48\text{\hspace{0.17em}in²}$

5. Tier 2 (7 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{38.48}{2}$$=19.24$$=19\text{\hspace{0.17em}servings}$

6. Tier 3 (5 in): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{5}{2}\right)}^2$$=19.63\text{\hspace{0.17em}in²}$

7. Tier 3 (5 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{19.63}{2}$$=9.82$$=9\text{\hspace{0.17em}servings}$

8. Add up the servings from every tier

   $39+19+9$$=67\text{\hspace{0.17em}servings}$

3. Servings: 34

1. Area of one square on top of the cake: 2 × 2 in

   $2\times 2$$=4\text{\hspace{0.17em}in²}$

2. Sheet cake: find the area of the top, since every slice uses its own patch of it

   $17\times 8$$=136\text{\hspace{0.17em}in²}$

3. Sheet cake: divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{136}{4}$$=34$$=34\text{\hspace{0.17em}servings}$

4. Servings: 34

1. Area of one square on top of the cake: 2 × 2 in

   $2\times 2$$=4\text{\hspace{0.17em}in²}$

2. Tier 1 (8 in): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{8}{2}\right)}^2$$=50.27\text{\hspace{0.17em}in²}$

3. Tier 1 (8 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{50.27}{4}$$=12.57$$=12\text{\hspace{0.17em}servings}$

4. Tier 2 (9 in): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{9}{2}\right)}^2$$=63.62\text{\hspace{0.17em}in²}$

5. Tier 2 (9 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{63.62}{4}$$=15.9$$=15\text{\hspace{0.17em}servings}$

6. Tier 3 (6 in): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{6}{2}\right)}^2$$=28.27\text{\hspace{0.17em}in²}$

7. Tier 3 (6 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{28.27}{4}$$=7.07$$=7\text{\hspace{0.17em}servings}$

8. Add up the servings from every tier

   $12+15+7$$=34\text{\hspace{0.17em}servings}$

5. Servings: 5

1. Area of one square on top of the cake: 2 × 2 in

   $2\times 2$$=4\text{\hspace{0.17em}in²}$

2. Sheet cake: find the area of the top, since every slice uses its own patch of it

   $19\times 8$$=152\text{\hspace{0.17em}cm²}$

3. Sheet cake: turn it into square inches to match the slice size (1 in² = 6.4516 cm²)

   $\frac{152}{6.4516}$$=23.56\text{\hspace{0.17em}in²}$

4. Sheet cake: divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{23.56}{4}$$=5.89$$=5\text{\hspace{0.17em}servings}$

6. Servings: 7

1. Area of one square on top of the cake: 2 × 2 in

   $2\times 2$$=4\text{\hspace{0.17em}in²}$

2. Tier 1 (11 cm): find the area of the top, since every slice uses its own patch of it

   ${11}^2$$=121\text{\hspace{0.17em}cm²}$

3. Tier 1 (11 cm): turn it into square inches to match the slice size (1 in² = 6.4516 cm²)

   $\frac{121}{6.4516}$$=18.76\text{\hspace{0.17em}in²}$

4. Tier 1 (11 cm): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{18.76}{4}$$=4.69$$=4\text{\hspace{0.17em}servings}$

5. Tier 2 (8 cm): find the area of the top, since every slice uses its own patch of it

   $8^2$$=64\text{\hspace{0.17em}cm²}$

6. Tier 2 (8 cm): turn it into square inches to match the slice size (1 in² = 6.4516 cm²)

   $\frac{64}{6.4516}$$=9.92\text{\hspace{0.17em}in²}$

7. Tier 2 (8 cm): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{9.92}{4}$$=2.48$$=2\text{\hspace{0.17em}servings}$

8. Tier 3 (6 cm): find the area of the top, since every slice uses its own patch of it

   $6^2$$=36\text{\hspace{0.17em}cm²}$

9. Tier 3 (6 cm): turn it into square inches to match the slice size (1 in² = 6.4516 cm²)

   $\frac{36}{6.4516}$$=5.58\text{\hspace{0.17em}in²}$

10. Tier 3 (6 cm): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

    $\frac{5.58}{4}$$=1.4$$=1\text{\hspace{0.17em}servings}$

11. Add up the servings from every tier

    $4+2+1$$=7\text{\hspace{0.17em}servings}$

7. Servings: 42

1. Area of one square on top of the cake: 2 × 2 in

   $2\times 2$$=4\text{\hspace{0.17em}in²}$

2. Tier 1 (9 in): find the area of the top, since every slice uses its own patch of it

   $9^2$$=81\text{\hspace{0.17em}in²}$

3. Tier 1 (9 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{81}{4}$$=20.25$$=20\text{\hspace{0.17em}servings}$

4. Tier 2 (8 in): find the area of the top, since every slice uses its own patch of it

   $8^2$$=64\text{\hspace{0.17em}in²}$

5. Tier 2 (8 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{64}{4}$$=16$$=16\text{\hspace{0.17em}servings}$

6. Tier 3 (5 in): find the area of the top, since every slice uses its own patch of it

   $5^2$$=25\text{\hspace{0.17em}in²}$

7. Tier 3 (5 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{25}{4}$$=6.25$$=6\text{\hspace{0.17em}servings}$

8. Add up the servings from every tier

   $20+16+6$$=42\text{\hspace{0.17em}servings}$

8. Servings: 33

1. Area of one square on top of the cake: 2 × 2 in

   $2\times 2$$=4\text{\hspace{0.17em}in²}$

2. Tier 1 (9 in): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{9}{2}\right)}^2$$=63.62\text{\hspace{0.17em}in²}$

3. Tier 1 (9 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{63.62}{4}$$=15.9$$=15\text{\hspace{0.17em}servings}$

4. Tier 2 (7 in): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{7}{2}\right)}^2$$=38.48\text{\hspace{0.17em}in²}$

5. Tier 2 (7 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{38.48}{4}$$=9.62$$=9\text{\hspace{0.17em}servings}$

6. Tier 3 (7 in): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{7}{2}\right)}^2$$=38.48\text{\hspace{0.17em}in²}$

7. Tier 3 (7 in): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{38.48}{4}$$=9.62$$=9\text{\hspace{0.17em}servings}$

8. Add up the servings from every tier

   $15+9+9$$=33\text{\hspace{0.17em}servings}$

9. Servings: 14

1. Area of one slice on top of the cake: 1 × 2 in

   $1\times 2$$=2\text{\hspace{0.17em}in²}$

2. Tier 1 (11 cm): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{11}{2}\right)}^2$$=95.03\text{\hspace{0.17em}cm²}$

3. Tier 1 (11 cm): turn it into square inches to match the slice size (1 in² = 6.4516 cm²)

   $\frac{95.03}{6.4516}$$=14.73\text{\hspace{0.17em}in²}$

4. Tier 1 (11 cm): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{14.73}{2}$$=7.37$$=7\text{\hspace{0.17em}servings}$

5. Tier 2 (11 cm): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{11}{2}\right)}^2$$=95.03\text{\hspace{0.17em}cm²}$

6. Tier 2 (11 cm): turn it into square inches to match the slice size (1 in² = 6.4516 cm²)

   $\frac{95.03}{6.4516}$$=14.73\text{\hspace{0.17em}in²}$

7. Tier 2 (11 cm): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{14.73}{2}$$=7.37$$=7\text{\hspace{0.17em}servings}$

8. Tier 3 (4 cm): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{4}{2}\right)}^2$$=12.57\text{\hspace{0.17em}cm²}$

9. Tier 3 (4 cm): turn it into square inches to match the slice size (1 in² = 6.4516 cm²)

   $\frac{12.57}{6.4516}$$=1.95\text{\hspace{0.17em}in²}$

10. Tier 3 (4 cm): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

    $\frac{1.95}{2}$$=0.97$$=0\text{\hspace{0.17em}servings}$

11. Add up the servings from every tier

    $7+7+0$$=14\text{\hspace{0.17em}servings}$

10. Servings: 16

1. Area of one slice on top of the cake: 1 × 2 in

   $1\times 2$$=2\text{\hspace{0.17em}in²}$

2. Tier 1 (14 cm): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{14}{2}\right)}^2$$=153.94\text{\hspace{0.17em}cm²}$

3. Tier 1 (14 cm): turn it into square inches to match the slice size (1 in² = 6.4516 cm²)

   $\frac{153.94}{6.4516}$$=23.86\text{\hspace{0.17em}in²}$

4. Tier 1 (14 cm): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{23.86}{2}$$=11.93$$=11\text{\hspace{0.17em}servings}$

5. Tier 2 (6 cm): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{6}{2}\right)}^2$$=28.27\text{\hspace{0.17em}cm²}$

6. Tier 2 (6 cm): turn it into square inches to match the slice size (1 in² = 6.4516 cm²)

   $\frac{28.27}{6.4516}$$=4.38\text{\hspace{0.17em}in²}$

7. Tier 2 (6 cm): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

   $\frac{4.38}{2}$$=2.19$$=2\text{\hspace{0.17em}servings}$

8. Tier 3 (8 cm): find the area of the top, since every slice uses its own patch of it

   $\pi \times {\left(\frac{8}{2}\right)}^2$$=50.27\text{\hspace{0.17em}cm²}$

9. Tier 3 (8 cm): turn it into square inches to match the slice size (1 in² = 6.4516 cm²)

   $\frac{50.27}{6.4516}$$=7.79\text{\hspace{0.17em}in²}$

10. Tier 3 (8 cm): divide by the area of one slice, then round down, since a leftover sliver isn't a serving

    $\frac{7.79}{2}$$=3.9$$=3\text{\hspace{0.17em}servings}$

11. Add up the servings from every tier

    $11+2+3$$=16\text{\hspace{0.17em}servings}$