sand is being poured from one container to another. The sand flows from the shaded part to the the unshaded cone. The shaded part is full of sand. The sand empties into the unshaded cone and fills it to the top. What is the height of the unshaded cone?
Shaded = 5cm radius / 4 cm + 2cm height
Unshaded = 6 cm radius
Possible answers are:
6.0 cm
8.3 cm
9.7 cm
12.5
ya umm u said possible answers are 6, 8.3, 9.7 and 12.5 but then u got an answer thats not even one of them. please explain
To determine the height of the unshaded cone, we need to compare the volumes of the shaded and unshaded regions.
The volume of a cone can be calculated using the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height.
Let's first calculate the volume of the shaded region:
V_shaded = (1/3) * π * (5cm)^2 * 2cm
= (1/3) * π * 25cm^2 * 2cm
= (1/3) * 50π cm^3
≈ 52.36 cm^3
Now, let's calculate the volume of the unshaded cone:
V_unshaded = (1/3) * π * (6cm)^2 * h
= (1/3) * π * 36cm^2 * h
= 12πh cm^3
Since the shaded part is full and empties into the unshaded cone, the volume of the shaded region is equal to the volume of the unshaded cone:
52.36 cm^3 = 12πh cm^3
Now, we can solve for h:
h = 52.36 cm^3 / (12π cm^3)
h ≈ 1.38 cm
Therefore, the height of the unshaded cone is approximately 1.38 cm.
None of the given answer choices match this result, so it's possible that there is an error in the question or answer options.
To find the height of the unshaded cone, we need to analyze the volume of sand that is poured from the shaded part to the unshaded cone.
First, let's find the volume of the shaded part. We have the radius of 5 cm and the height of 2 cm. The volume of a cone is given by the formula: V = (1/3) * π * r^2 * h.
Using the formula, the volume of the shaded part is: V_shaded = (1/3) * π * (5^2) * 2 = (1/3) * π * 25 * 2 = (50/3) * π cm^3.
Now, let's consider the unshaded cone. We are told that the sand fills the unshaded cone completely, so the volume of the shaded part must be equal to the volume of the unshaded cone.
The volume of the unshaded cone is given by: V_unshaded = (1/3) * π * (6^2) * h_unshaded.
Since V_shaded = V_unshaded, we can set up the equation:
(50/3) * π = (1/3) * π * (6^2) * h_unshaded.
Canceling out π and simplifying, we get:
(50/3) = 36 * h_unshaded.
Solving for h_unshaded, we have:
h_unshaded = (50/3) / 36 = 1.39 cm (rounded to two decimal places).
Therefore, the height of the unshaded cone is approximately 1.39 cm.
However, none of the possible answers provided match this result. Please review the given information and options to ensure they align correctly.
Not sure what that description means, but if it is a cylinder atop a cone of radius 5 and height 4, then its volume is
π/3 * 5^2 * 4 + π * 5^2 * 2 = 250π/3
So, the bottom cone must have the same volume:
π/3 * 6^2 h = 250π/3
36h = 250
h = 250/36 = 6.9 cm