Question

Betsy has chosen a set of vases for her wedding registry. The vases are cylindrical and their dimensions (in inches) are as follows.

• Vase A: h = 14 and r = 3
• Vase B: h = 7 and r = 6

Which of the following statements about the volumes of the vases is true?
The volume of vase A is half the volume of vase B.
The volume of vase B is half the volume of vase A.
The volume of vase B is four times the volume of vase A.
The volumes of the two vases are equal.

Answer 1

@satellite73

Answer 2

\(\large {
\textit{volume of a cylinder}= \pi r^2 h
\begin{cases}
h=14\quad r=3\to \pi\cdot 14^2\cdot 3
\\ \quad \\
h=7\quad r=6\to \pi \cdot 7^2\cdot 6
\end{cases}
\\ \quad \\
\cfrac{\pi\cdot 14^2\cdot 3}{\pi \cdot 7^2\cdot 6}\implies \cfrac{\pi\cdot (2\cdot 7)^2\cdot 3}{\pi \cdot 7^2\cdot 2\cdot 3}
\implies \cfrac{\pi\cdot (2\cdot 7)(2\cdot 7)\cdot 3}{\pi \cdot 7\cdot 7\cdot2\cdot 3}
\\ \quad \\
\cfrac{\pi\cdot 2\cdot 7\cdot 2\cdot 7\cdot 3}{\pi \cdot 7\cdot 7\cdot2\cdot 3}
}\)

what do you think?

Answer 3

volume of one over the other
would give you the ratio of "one" over the "other"

Answer 4

c or b i think

Answer 5

well, what does the fraction simplify to?

Answer 6

c i think

Answer 7

well, the fraction has no variable "c", so... it wouldn't simplify to that

Answer 8

Im confused

Answer 9

what is the volume of vase A?

use the formula V = pi*r^2*h

Answer 10

you're asked on what is the "ratio" of one of the vases in relation to the other
is it half, one third whatever else
thus
is a ratio matter, or, what is the ratio of one vase in relation to the other

thus "a" in relation to "b" would be a:b or \(\frac{a}{b}\)

Answer 11

okay