Question

the volume of a cylinder is the base (b) times the length of its height (h). which of the following is the formula for the volume of a cylinder? a. v = 2bw b. v = \frac{1}{2}bh c. v = -bh d. v = bh

Explanation:

Step1: Analyze the problem statement

The problem states that the volume of a cylinder is the base (\( B \)) times the height (\( h \)).

Step2: Check each option

• Option A: \( V = 2Bw \) has an extra variable \( w \) which is not mentioned in the problem statement (volume should be related to base and height only), so it is incorrect.
• Option B: \( V=\frac{1}{2}Bh \) has a coefficient \(\frac{1}{2}\). But there is no such factor in the description (volume is just base times height), so it is incorrect.
• Option C: \( V=-Bh \) has a negative sign. Volume cannot be negative in this context (as it is a measure of space occupied and \( B\) (area of base) and \( h\) (height) are non - negative quantities), so it is incorrect.
• Option D: \( V = Bh \) directly follows the description "the volume of a cylinder is the base (\( B \)) times the length of its height (\( h \))", so it is correct.

Answer:

D. \( V = Bh \)