Question

The weight of a can of soup varies jointly with the height and the square of the diameter. a can 8 inches high with a diameter of 3 inches weighs 28.8 ounces. what is the weight of a can that is 4 inches high with a diameter of 2 ​inches?

Answer 1

The correct answer is 6.4 ounces. 

In order to find the weight of the can, you first must find the constant that the variation is expressed with. All direct variations are the two variables multiplied together and then by a constant that does not change from equation to equation. In this case, we'll use k to stand for the constant and solve. 

w = kh$\d^{2}$
28.8 = k(8)(9)
28.8 = 72k
.4 = k

Now that we know .4 = k, we can use the same equation to find the new weight.

w = kh$\d^{2}$
w = (.4)(4)(4)
w = 6.4 

Answer 2

Answer:

The weight of the is 6.4 ounces.

Step-by-step explanation:

Given,

The weight of a can of soup varies jointly with the height and the square of the diameter,

⇒ Weight ∝ (Height).(Diameter)²

Let w represents weight in ounces , h represents height and d represents the diameter,

⇒ w ∝ (h)(d)²

$\implies w = k(h)(d)^2$ -----(1)

Where, k is the constant of proportionality,

Now, according to the question,

For, h = 8 in, d = 3 in, w = 28.8 ounces,

From equation (1),

$28.8 = k(8)(3)^2$

$28.8 = 72k$

$\implies k=\frac{28.8}{72}=0.4$

Thus, from equation (1),

$w=0.4(h)(d)^2$

For, h = 4 in, d = 2 in,

Weight of the can,

$w=0.4\times 4\times 2^2=1.6\times 4=6.4\text{ ounces}$