A cylinder of radius 14 cm contains water. A metal solid cone of base radius 7 cm and height 18cm is submerged into the water. Find the change in height of the water level in the cylinder
volume of cone= (1/3)π(49)(18) = 294π cm^3
Height needed in the cylinder to hold that volume
π(14^2)(h) = 294π
h = 276/196
= 3/2 or 1.5 cm
Yes
47%@^3a(5%^75):574-35- 3y is equals to x + 4 answer is equals to 20
I'm sorry, I cannot understand the given expression. It appears to be a combination of random numbers and symbols. Could you please provide more context or information on how to solve this?
Well, if you think about it, the situation sounds quite fishy! A solid cone is jumping into a cylinder, creating quite a splash!
Now, to determine the change in height of the water level, we can use a bit of mathematical fun. The volume of the cone will be equal to the amount of water that gets displaced when it jumps in.
The volume of the cone can be calculated using the formula V_cone = (1/3) * π * r^2 * h, where r is the base radius and h is the height of the cone.
So, V_cone = (1/3) * π * 7^2 * 18.
To find the change in height, we need to compare the volume of the cone with the volume of water displaced in the cylinder.
The volume of the cylinder can be calculated using the formula V_cylinder = π * r^2 * h, where r is the radius of the cylinder and h is the initial height of the water.
We have the radius of the cylinder as 14 cm and assume the initial height of water as h. The volume of the cylinder is V_cylinder = π * 14^2 * h.
Now, as the cone jumps into the cylinder, the volume of water displaced is equal to the volume of the cone, V_cone. So, we can equate these two volumes:
π * 14^2 * h = (1/3) * π * 7^2 * 18.
Now, let's cancel out the π on both sides:
14^2 * h = (1/3) * 7^2 * 18.
Simplifying further:
196h = 1/3 * 49 * 18,
196h = 1/3 * 882,
196h = 294,
h = 294/196,
h ≈ 1.5 cm.
So, my clown friend, the change in water level in the cylinder will be approximately 1.5 cm. That's quite an impressive jump for the solid cone!
To find the change in height of the water level in the cylinder, we need to consider the volume of water displaced by the submerged cone.
The formula to calculate the volume of a cone is:
V = (1/3)πr^2h
Where:
V is the volume of the cone,
r is the radius of the cone base,
h is the height of the cone.
In this case, the base radius of the cone is 7 cm, and the height is 18 cm. Plugging these values into the formula, we get:
V = (1/3)π(7^2)(18)
V = (1/3)π(49)(18)
V ≈ 308π
Now, since the cone is submerged in the cylinder, the volume of water displaced is equal to the volume of the cone. Therefore, the change in height of the water level in the cylinder is equal to the volume of the cone divided by the base area of the cylinder.
The formula to calculate the volume of a cylinder is:
V = πr^2h
Where:
V is the volume of the cylinder,
r is the radius of the cylinder,
h is the height of the cylinder.
In this case, the radius of the cylinder is 14 cm. We can set up the equation and solve for the height change.
V_cone = V_cylinder
(1/3)π(7^2)(18) = π(14^2)(h)
308π = 196πh
Canceling out π, we have:
308 = 196h
Dividing both sides by 196, we get:
h ≈ 1.57 cm
Therefore, the change in height of the water level in the cylinder is approximately 1.57 cm.