a vase is in the shape of a cone that is 10 inches tall with a diameter of 3 inches. what is the greatest amount of water the vase can hold
a.) 23.56 in.^3
b.) 54.72 in.^3
c.) 70.65 in.^3
d.) 94.25 in.^3
SDCISFBDS people from the past.....i miss the old days, RIP
@ms.sue
Well, let me just put on my comedy hat for this one!
A vase shaped like a cone, huh? Sounds like a pun waiting to happen.
Okay, let's get serious for a moment. To find the volume of a cone, we use the formula V = (1/3) π r^2 h, where r is the radius and h is the height.
Given that the diameter is 3 inches, we know that the radius is half of that, so the radius is 1.5 inches. And the height is 10 inches.
Plugging these values into the formula, we get V = (1/3) π (1.5^2) (10) = 23.56 in.^3
So, the answer is a.) 23.56 in.^3. Now, wasn't that a barrel of laughs?
To find the greatest amount of water the vase can hold, we need to calculate its volume.
The volume of a cone can be calculated using the formula V = (1/3) * π * r^2 * h, where V is the volume, π is approximately 3.14159, r is the radius of the base, and h is the height of the cone.
Given that the height of the cone is 10 inches and the diameter (which is twice the radius) is 3 inches, we can calculate the radius by dividing the diameter by 2:
radius = diameter / 2 = 3 inches / 2 = 1.5 inches.
Now we can plug in the values into the formula:
V = (1/3) * 3.14159 * (1.5 inches)^2 * 10 inches.
Calculating this expression:
V = (1/3) * 3.14159 * 2.25 square inches * 10 inches.
Simplifying:
V = 7.8548 square inches * 10 inches * (1/3).
V = 78.548 cubic inches * (1/3).
V ≈ 26.18 cubic inches.
Therefore, the greatest amount of water the vase can hold is approximately 26.18 cubic inches.
Comparing this value to the options provided:
a.) 23.56 in.^3
b.) 54.72 in.^3
c.) 70.65 in.^3
d.) 94.25 in.^3
The closest option to 26.18 cubic inches is option a.) 23.56 in.^3, but it is smaller. Therefore, the correct answer is none of the options provided.