Maria has baked a cake for Cathy's birthday. The dimensions of the cake are 13/1/2 inches by 6/3/4 inches. The cake is going to be cut into squares with each piece being approximately 5.55% of the cake, which should give a total of _______
pieces of cake with each piece having a side length of __________
inches.
5.55% = 1/18
so, cut the cake into 18 equal squares.
The cake is twice as long as it is wide, so that means cut half the cake (6 3/4 x 6 3/4) into 9 pieces, each with a side of 1/3 * 6 3/4 = 2 1/4 inches.
Mandana is ordering new tile for her kitchen floor. The area of the floor is 113.5 square feet, and she wants to order between 15% and 20% extra of the materials. Which of the following is a reasonable amount of tile for Mandana to order?
137 square feet
132 square feet
129 square feet
127 square feet
To find the total number of pieces of cake, we first need to calculate the area of the cake.
Area of the cake = length * width
The length of the cake is 13 1/2 inches, which can be written as 13 + 1/2 = 13.5 inches.
The width of the cake is 6 3/4 inches, which can be written as 6 + 3/4 = 6.75 inches.
Area of the cake = 13.5 inches * 6.75 inches
To calculate the total number of pieces of cake, we need to divide the area of the cake by the area of each square piece.
Area of each square piece = (5.55/100) * Area of the cake
Total number of pieces of cake = Area of the cake / Area of each square piece
Now let's calculate the values:
Area of the cake = 13.5 inches * 6.75 inches
Area of each square piece = (5.55/100) * Area of the cake
Total number of pieces of cake = Area of the cake / Area of each square piece
To find the number of pieces of cake and the side length of each piece, we can follow these steps:
1. Calculate the area of the cake:
- To find the area, multiply the length by the width.
- Length: 13 1/2 inches = 13.5 inches
- Width: 6 3/4 inches = 6.75 inches
- Area = Length × Width
2. Calculate the size of each piece:
- Multiply the area of the cake by 5.55% (0.0555) to find the area of each piece.
3. Calculate the number of pieces:
- Divide the area of the cake by the area of each piece to find the number of pieces.
Let's proceed with the calculations:
1. Calculate the area of the cake:
Area = Length × Width
Area = 13.5 inches × 6.75 inches
Area = 91.125 square inches
2. Calculate the size of each piece:
Piece Area = Area × 0.0555
Piece Area = 91.125 square inches × 0.0555
Piece Area ≈ 5.06 square inches (rounded to two decimal places)
3. Calculate the number of pieces:
Number of Pieces = Area ÷ Piece Area
Number of Pieces = 91.125 square inches ÷ 5.06 square inches
Number of Pieces ≈ 18 (rounded to the nearest whole number)
Therefore, the total number of pieces of cake will be approximately 18, and each piece will have a side length of approximately √(5.06) square inches (rounded to two decimal places).