After school, Carlos helps his mom at her cake shop, Love and Lace Cakes. Today, he is helping her bake a 3-layer wedding cake. Each layer will be 2 1/2 inches tall and shaped like a rectangular prism. The bottom layer will be 12 inches long and 10 inches wide. The middle layer will be 10 inches long and 8 inches wide. The top layer will be 8 inches long and 6 inches wide. What will the total volume of the wedding cake be?
The volume of each layer is found by multiplying the length times the width times the height: 12 inches * 10 inches * 2.5 inches = <<12*10*2.5=300>>300 cubic inches for the bottom layer.
10 inches * 8 inches * 2.5 inches = <<10*8*2.5=200>>200 cubic inches for the middle layer.
8 inches * 6 inches * 2.5 inches = <<8*6*2.5=120>>120 cubic inches for the top layer.
The total volume of the cake is found by adding the volumes of each layer together: 300 cubic inches + 200 cubic inches + 120 cubic inches = <<300+200+120=620>>620 cubic inches. Answer: \boxed{620}.
To find the volume of each layer, we need to multiply the length, width, and height together.
For the bottom layer:
Length = 12 inches
Width = 10 inches
Height = 2 1/2 inches = 5/2 inches
Volume = Length × Width × Height
Volume = 12 inches × 10 inches × 5/2 inches
To simplify the fraction, we can multiply the numerator and denominator by 2:
Volume = 12 inches × 10 inches × (5/2 inches) × (2/2)
Volume = 12 inches × 10 inches × 10/4 inches
Volume = 120 inches × 2.5 inches
Volume = 300 cubic inches
The volume of the bottom layer is 300 cubic inches.
For the middle layer:
Length = 10 inches
Width = 8 inches
Height = 2 1/2 inches = 5/2 inches
Volume = Length × Width × Height
Volume = 10 inches × 8 inches × 5/2 inches
To simplify the fraction, we can multiply the numerator and denominator by 2:
Volume = 10 inches × 8 inches × (5/2 inches) × (2/2)
Volume = 10 inches × 8 inches × 10/4 inches
Volume = 80 inches × 2.5 inches
Volume = 200 cubic inches
The volume of the middle layer is 200 cubic inches.
For the top layer:
Length = 8 inches
Width = 6 inches
Height = 2 1/2 inches = 5/2 inches
Volume = Length × Width × Height
Volume = 8 inches × 6 inches × 5/2 inches
To simplify the fraction, we can multiply the numerator and denominator by 2:
Volume = 8 inches × 6 inches × (5/2 inches) × (2/2)
Volume = 8 inches × 6 inches × 10/4 inches
Volume = 48 inches × 2.5 inches
Volume = 120 cubic inches
The volume of the top layer is 120 cubic inches.
To find the total volume of the wedding cake, we need to add up the volumes of each layer:
Total Volume = Volume of Bottom Layer + Volume of Middle Layer + Volume of Top Layer
Total Volume = 300 cubic inches + 200 cubic inches + 120 cubic inches
Total Volume = 620 cubic inches
The total volume of the wedding cake is 620 cubic inches.