Question Which volume formula(s) show(s) a joint variation? $V=s^{3}$ , $V=\pi r^{2} h$ , or $V=B h$ ?

Studdy Solution

STEP 1

Assumptions1. We are given three volume formulas I. $V=s^{3}$ II. $V=\pi r^{} h$ III. $V=B h$ . We need to determine which of these formulas show a joint variation.

STEP 2

First, let's define what joint variation means. Joint variation (or combined variation) is a form of direct variation where a quantity varies directly as the product of two (or more) other quantities.
In mathematical terms, if y varies jointly as x and z, then the equation is of the form $y = kxz$ where k is the constant of variation.

STEP 3

Let's analyze each formula to see if it fits this pattern.
. $V=s^{3}$ This formula does not show a joint variation because the volume V varies with the cube of s, not the product of two or more different quantities.

STEP 4

II. $V=\pi r^{2} h$
This formula does show a joint variation because the volume V varies directly as the product of the square of r and h.

STEP 5

III. $V=B h$
This formula also shows a joint variation because the volume V varies directly as the product of B and h.

STEP 6

So, the formulas that show a joint variation are II and III only.
Therefore, the correct answer is "II and III only".

Was this helpful?

Question Which volume formula(s) show(s) a joint variation? $V=s^{3}$ , $V=\pi r^{2} h$ , or $V=B h$ ?

Studdy Solution

STEP 1

Assumptions1. We are given three volume formulas I. $V=s^{3}$ II. $V=\pi r^{} h$ III. $V=B h$ . We need to determine which of these formulas show a joint variation.

STEP 2

STEP 3

Let's analyze each formula to see if it fits this pattern.
. $V=s^{3}$ This formula does not show a joint variation because the volume V varies with the cube of s, not the product of two or more different quantities.

STEP 4

II. $V=\pi r^{2} h$
This formula does show a joint variation because the volume V varies directly as the product of the square of r and h.

STEP 5

III. $V=B h$
This formula also shows a joint variation because the volume V varies directly as the product of B and h.

STEP 6

So, the formulas that show a joint variation are II and III only.
Therefore, the correct answer is "II and III only".

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question Which volume formula(s) show(s) a joint variation? V=s3V=s^{3}V=s3, V=πr2hV=\pi r^{2} hV=πr2h, or V=BhV=B hV=Bh?

Studdy Solution

STEP 1

Assumptions1. We are given three volume formulas I. V=s3V=s^{3}V=s3 II. V=πrhV=\pi r^{} hV=πrh III. V=BhV=B hV=Bh . We need to determine which of these formulas show a joint variation.

STEP 2

STEP 3

Let's analyze each formula to see if it fits this pattern.. V=s3V=s^{3}V=s3This formula does not show a joint variation because the volume V varies with the cube of s, not the product of two or more different quantities.

STEP 4

II. V=πr2hV=\pi r^{2} hV=πr2hThis formula does show a joint variation because the volume V varies directly as the product of the square of r and h.

STEP 5

III. V=BhV=B hV=BhThis formula also shows a joint variation because the volume V varies directly as the product of B and h.

STEP 6

So, the formulas that show a joint variation are II and III only.Therefore, the correct answer is "II and III only".

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question Which volume formula(s) show(s) a joint variation? $V=s^{3}$ , $V=\pi r^{2} h$ , or $V=B h$ ?

Assumptions1. We are given three volume formulas I. $V=s^{3}$ II. $V=\pi r^{} h$ III. $V=B h$ . We need to determine which of these formulas show a joint variation.

Let's analyze each formula to see if it fits this pattern.
. $V=s^{3}$ This formula does not show a joint variation because the volume V varies with the cube of s, not the product of two or more different quantities.

II. $V=\pi r^{2} h$
This formula does show a joint variation because the volume V varies directly as the product of the square of r and h.

III. $V=B h$
This formula also shows a joint variation because the volume V varies directly as the product of B and h.

So, the formulas that show a joint variation are II and III only.
Therefore, the correct answer is "II and III only".