Theresa 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? V^cylinder=πr^2h answer choices are as follow: A.
The volume of vase B is four times the volume of vase A.
B.
The volumes of the two vases are equal.
C.
The volume of vase B is half the volume of vase A.
D.
The volume of vase A is half the volume of vase B.
C. The volume of vase B is half the volume of vase A.
To calculate the volume of each vase, we can use the formula V = πr^2h for a cylinder.
For vase A:
V = π(2)^2(14) = 56π
For vase B:
V = π(4)^2(7) = 112π
Dividing the volume of vase B by the volume of vase A, we get:
112π / 56π = 2
Therefore, the volume of vase B is twice the volume of vase A, which means that the correct statement is that the volume of vase B is half the volume of vase A.
it was D
I apologize for the error in my previous response. You are correct that the answer is D.
The volume of vase A is:
V(A) = π(2)^2(14) = 56π
The volume of vase B is:
V(B) = π(4)^2(7) = 112π
Dividing the volume of vase A by the volume of vase B, we get:
56π / 112π = 1/2
Therefore, the correct statement is that the volume of vase A is half the volume of vase B.
To determine which statement about the volumes of the vases is true, we need to calculate the volumes of vase A and vase B and compare them.
The formula for the volume of a cylindrical vase is given as V = πr^2h, where r is the radius of the base and h is the height of the vase.
For vase A:
Radius (r) = 2 inches
Height (h) = 14 inches
Vase A volume = π * (2^2) * 14
= π * 4 * 14
= 56π cubic inches
For vase B:
Radius (r) = 4 inches
Height (h) = 7 inches
Vase B volume = π * (4^2) * 7
= π * 16 * 7
= 112π cubic inches
Now let's compare the volumes of the vases:
56π (volume of vase A) versus 112π (volume of vase B)
Since the volumes are not the same, we can eliminate option B.
To determine whether the volume of vase B is four times the volume of vase A (option A) or if the volume of vase B is half the volume of vase A (option C) or vice versa (option D), let's evaluate the ratios:
Volume of vase B/Volume of vase A = 112π/56π = 2
Since the ratio is 2, we can conclude that the volume of vase B is two times the volume of vase A, and therefore, option C is correct.
Therefore, the statement that is true is: "C. The volume of vase B is half the volume of vase A."