To determine the correct formula for the volume of a cylinder, let's break down the elements involved in finding the volume.
The volume of a cylinder can be found by multiplying the area of the base (denoted as [tex]\( B \)[/tex]) by the height (denoted as [tex]\( h \)[/tex]).
Given the question with the options:
A. [tex]\( V = -B h \)[/tex]
B. [tex]\( V = 2 B w \)[/tex]
C. [tex]\( V = \frac{1}{2} B h \)[/tex]
D. [tex]\( V = B h \)[/tex]
Let's analyze each option:
1. Option A: [tex]\( V = -B h \)[/tex]
- This formula shows a negative sign before [tex]\( B h \)[/tex]. The volume of a cylinder, being a measurement of physical space, cannot be negative. Hence, this cannot be correct.
2. Option B: [tex]\( V = 2 B w \)[/tex]
- This formula multiples the base area [tex]\( B \)[/tex] with [tex]\( 2 \)[/tex] and another variable [tex]\( w \)[/tex]. Here, [tex]\( w \)[/tex] doesn't represent height, making this an incorrect relationship for the volume of a cylinder.
3. Option C: [tex]\( V = \frac{1}{2} B h \)[/tex]
- This formula effectively halves the product of [tex]\( B \)[/tex] and [tex]\( h \)[/tex]. The volume calculation should involve the entire product of the base and height without factoring it down. Thus, this is incorrect.
4. Option D: [tex]\( V = B h \)[/tex]
- This formula correctly multiplies the base area [tex]\( B \)[/tex] by height [tex]\( h \)[/tex], which accurately represents the volume of the cylinder.
Therefore, the correct formula for the volume of a cylinder is:
[tex]\[ V = B h \][/tex]
The correct choice is:
D. [tex]\( V = B h \)[/tex]
