A cone shaped vessel has a height of twice its radius. If I fill the vessel with water to a depth of 10 cm, find the volume of water to the nearest cm^3.
Answer is 262
Volume of cone formula
V = π (r^2) (h / 3)
For your cone:
V = π (5^2) (10 / 3)
= 261.799387799
To find the volume of water in the cone-shaped vessel, we need to first find the radius and height of the cone.
Let's assume that the radius of the cone is "r" and the height is "h".
According to the given information, the height of the cone is twice its radius. So, we can write:
h = 2r
We also know that the vessel is filled with water to a depth of 10 cm. This means that the height of the water in the cone is 10 cm. So, we can write:
h = 10
Now, let's substitute the value of h into the first equation:
10 = 2r
To find the value of "r", we can simply solve this equation:
r = 10 / 2
r = 5 cm
Now that we have the value of the radius, we can find the volume of the cone using the formula:
Volume = (1/3) * pi * r^2 * h
Substituting the values, we get:
Volume = (1/3) * 3.14 * (5^2) * 10
Volume = (1/3) * 3.14 * 25 * 10
Volume = 261.67 cm^3
Rounding this value to the nearest cm^3, we get the final answer:
Volume ≈ 262 cm^3