Question

Jodie 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 = 2
• Vase B: h = 7 and r = 4

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

Answer 1

To determine which statement is true regarding the volumes of the vases, we can use the formula for the volume of a cylinder:

\[
V = \pi r^2 h
\]

Now we will calculate the volumes of both vases, A and B.

**Volume of Vase A:**
- Height (h) = 14 inches
- Radius (r) = 2 inches

\[
V_A = \pi r^2 h = \pi (2^2)(14) = \pi (4)(14) = 56\pi
\]

**Volume of Vase B:**
- Height (h) = 7 inches
- Radius (r) = 4 inches

\[
V_B = \pi r^2 h = \pi (4^2)(7) = \pi (16)(7) = 112\pi
\]

Now we have the volumes:
- Volume of Vase A, \( V_A = 56\pi \)
- Volume of Vase B, \( V_B = 112\pi \)

Now, let's check each of the statements:

A. The volume of vase B is twice the volume of vase A.

\[
2 V_A = 2(56\pi) = 112\pi = V_B \quad \text{(True)}
\]

B. The volume of vase A is twice the volume of vase B.

\[
2 V_B = 2(112\pi) = 224\pi \quad \text{(False)}
\]

C. The volumes of the two vases are equal.

\[
V_A \neq V_B \quad \text{(False)}
\]

D. The volume of vase B is four times the volume of vase A.

\[
4 V_A = 4(56\pi) = 224\pi \quad \text{(False)}
\]

The correct statement is:

**A. The volume of vase B is twice the volume of vase A.**