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select the correct answer. The capacity of a circular bowl varies directly with the cube of its diameter. How does the capacity of the bowl change when the diameter is doubled? a. the capacity is multiplied by 8. b. the capacity is multiplied by 2. c. the capacity is multiplied by 1/8. d. the capacity is multiplied by 1/2.​

Respuesta :

Answer:

A

Step-by-step explanation:

got it right on the test

In a directly proportional relationship, increasing one variable will increase another. The correct option is A.

What is the directly proportional relationship?

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as

p∝q where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called the constant of proportionality.

Given that the capacity of a circular bowl varies directly with the cube of its diameter. Therefore, the relationship can be written as,

Volume of the bowl ∝ (Diameter of the bowl)³

V₁ ∝ (D)³

Now, if the diameter of the bowl is increased and made double. Then the volume of the bowl will be,

Volume ∝ (2 × Diameter)³

V₂ ∝ (2D)³

V₂ ∝ 8(D)³

V₂ ∝ 8 V₁

Thus, when the diameter is doubled then the capacity of the bowl changes to 8 times the initial.

Hence, the capacity is multiplied by 8.

Learn more about Directly proportional relationships:

https://brainly.com/question/13082482

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