Proportionality
If the side of a granite cube is 10 times that of another granite cube, the pressure exerted by the larger cube on its base is times the pressure exerted by the smaller cube on its base.
P correlation L
So what is the question?
Pressure=constant*(L)
Proof: weight=constant*L^3
basearea= constant2)L^2\
Pressure=weight/area= constant L^3/constant2 L^2= constant*L
The question
A granite cube is 10 times that of another granite cube. The pressure exerted by the larger cube on its base is how many times more the pressure exerted by the smaller cube on its base?
post it.
Henry,
What do mean its posted. I still need to figure out the answer
To solve this problem, we need to understand the concept of proportionality. In this case, we are dealing with two granite cubes, one larger than the other.
The pressure exerted by an object on its base depends on its weight (mass) and the surface area of the base. Mathematically, pressure (P) is defined as force (F) divided by area (A): P = F/A.
Now, let's consider the two granite cubes. Let's assume that the weight of the smaller cube is represented by W_1 and the weight of the larger cube is represented by W_2. Also, let the surface area of the base of the smaller cube be A_1 and the surface area of the base of the larger cube be A_2.
Since the cubes are made of granite, the density of both cubes is the same. Density (D) is defined as mass (M) divided by volume (V): D = M/V.
As both cubes are made of granite, their densities can be assumed to be the same. Hence, we have D_1 = D_2.
Now, let's represent the volumes of the smaller and larger cubes as V_1 and V_2, respectively. Since volume is directly proportional to the cube of the side length, we have V_1/V_2 = (L_1/L_2)^3.
Given that the side length of the larger cube is 10 times that of the smaller cube, we have L_2 = 10L_1.
Combining the above equations, we can write:
V_1/V_2 = (L_1/L_2)^3
V_1/V_2 = (L_1/10L_1)^3
V_1/V_2 = (1/10)^3
V_1/V_2 = 1/1000
As density (D) is equal to mass (M) divided by volume (V), we can express the weights of the cubes in terms of their volumes and densities:
W_1/V_1 = D_1
W_2/V_2 = D_2
Since both cubes have the same density, we can conclude that the weights are proportional to the volumes:
W_1/V_1 = W_2/V_2
Substituting V_1/V_2 = 1/1000, we have:
W_1/(1/1000) = W_2/1
W_1 = 1/1000 * W_2
W_1 = W_2/1000
Now, let's compare the pressures exerted by the cubes on their bases. Recall that pressure is defined as force divided by area:
P_1 = W_1/A_1
P_2 = W_2/A_2
Substituting the expression for W_1, we get:
P_1 = (W_2/1000)/A_1
To find the relationship between P_1 and P_2, we need to find the relationship between A_1 and A_2. Since the surface area of a square is proportional to the square of its side length, we have:
A_1/A_2 = (L_1/L_2)^2
A_1/A_2 = (L_1/10L_1)^2
A_1/A_2 = 1/100
Substituting this into the expression for P_1, we get:
P_1 = (W_2/1000)/(1/100) * P_1 = (W_2/10)
Therefore, the pressure exerted by the larger cube on its base is 1/10 times the pressure exerted by the smaller cube on its base (or P_1 = (1/10)P_2).