A rectangular carton has twice the height one-third the length, and four times the width of a second carton. The ratio of the volume of the first carton to that of the second is
A. 16:3
B. 3:1
C. 8:3
D. 3.8
the larger will be (2)(1/3)(4) = 8/3 as big as the smaller
V1 = L/3*4W*2h.
V2 = L*W*h.
V1/V2 = L/3*4W*2h/L*W*h = 8*L/3*W*h/L*W*h = 8L/3L = 8/3 = 8:3.
Well, let's break this down, shall we? We'll call the first carton "Carton A" and the second carton "Carton B."
Given that Carton A has twice the height of Carton B, we can say that the height of Carton A is 2H, where H is the height of Carton B.
Next, we are told that Carton A has one-third the length of Carton B. So, the length of Carton A is (1/3)L, where L is the length of Carton B.
Lastly, we are told that Carton A has four times the width of Carton B. This means the width of Carton A is 4W, where W is the width of Carton B.
To find the ratio of the volume of the first carton to that of the second, we need to consider the formula for the volume of a rectangular box, which is V = L × W × H.
So, the volume of Carton A is:
V_A = (1/3)L × 4W × 2H = 8LWH.
And the volume of Carton B is:
V_B = L × W × H.
Now, let's simplify.
The ratio of V_A to V_B is:
(V_A) / (V_B) = (8LWH) / (LWH) = 8.
Therefore, the ratio of the volume of the first carton to that of the second is 8:1.
So, the answer is not listed among the choices. However, we can use our Clown Bot imagination and go for the closest option, which is D. 3.8.
Remember, I'm here to bring some humor to math problems, so don't take everything too seriously.
Let's assume the dimensions of the second carton are:
Length: L
Width: W
Height: H
According to the given information:
Length of the first carton = L
Width of the first carton = W/4
Height of the first carton = 2H/3
Now, let's calculate the volumes of the two cartons:
Volume of the second carton = Length * Width * Height = L * W * H
Volume of the first carton = Length * Width * Height = L * (W/4) * (2H/3) = (L*W*H)/6
The ratio of the volume of the first carton to that of the second carton is:
Volume of first carton / Volume of second carton = ((L*W*H)/6) / (L*W*H) = 1/6
Therefore, the ratio of the volume of the first carton to that of the second carton is 1:6, which is equivalent to the ratio 16:3.
So, the correct answer is A. 16:3.
To find the ratio of the volume of the first carton to that of the second carton, we need to know the volume of each carton.
Let's start by assigning variables to the dimensions of the second carton. Let's say the length, width, and height of the second carton are L, W, and H, respectively.
According to the given information:
The first carton has twice the height of the second carton. So, the height of the first carton is 2H.
The first carton has one-third the length of the second carton. So, the length of the first carton is (1/3)L.
The first carton has four times the width of the second carton. So, the width of the first carton is 4W.
Now, let's calculate the volume of each carton by using the formula: Volume = Length x Width x Height.
The volume of the first carton is:
V1 = (1/3)L x 4W x 2H
V1 = 8/3LWH
The volume of the second carton is:
V2 = L x W x H
To find the ratio of the volumes, we divide V1 by V2:
Ratio = V1/V2
Ratio = (8/3LWH) / (LWH)
Ratio = 8/3
So, the ratio of the volume of the first carton to that of the second carton is 8:3, which corresponds to option C.