A tank in the shape of a cone has a diameter of 8 feet and a height of 10 feet.when there is water in the tank, th water is in the shape of a cone too. find the radius of the cone of water when the water is 2 feet high. Explain how you would solve it.
To find the radius of the cone of water when it is 2 feet high, you can use the similar triangles property.
First, let's calculate the radius of the original cone. Since the diameter is given as 8 feet, we can find the radius by dividing it by 2:
radius = diameter / 2 = 8ft / 2 = 4ft.
Now, let's find the height of the cone of water. Since the height of the original cone is 10 feet, and we want to find the radius when the water is 2 feet high, we need to find the proportion of the heights:
height of water / height of original cone = radius of water / radius of original cone.
Plugging in the given values, we have:
2ft / 10ft = radius of water / 4ft.
Now, we can solve for the radius of the water cone:
radius of water = (2ft / 10ft) * 4ft.
Multiplying and simplifying, we get:
radius of water = 0.8ft.
Therefore, the radius of the cone of water when it is 2 feet high is 0.8 feet.
first, imagine the front view of the cone,, it should look like an inverted triangle,, then draw the content (the water - horizontal line),, note that if you draw a vertical line bisecting the inverted triangle, you actually form a right triangle,,
since you bisected it, get the radius: r= d/2 = 8/2 = 4 feet
then draw another horizontal line for which height is 2 feet,,
recall similar triangles,, you just have to do ration and proportion of the base and height,, therefore:
let x = radius when height is 2 feet
4/x=10/2
x= 4/5 or 0.8 feet
so there,, =)