I can't figure this out

Question

A barrel with a diameter of 32 inches has a height of 4 feet. It is partially filled with water and when the barrel is lying on its side, the water has a depth of 8 inches. Find the volume of the water to the hundredth place

Answer 1

Hi Zicheng,

 

Try this and see if it helps get you going in the right direction.

 

Picture looking at the barrel from one of its ends. The cross section will be a circle with radius 16 in. Draw a horizontal line parallel to the ground that is 8 inches above where the barrel touches the ground. The represents the depth of the water. Now draw radii to the points where the drawn line intersects the circle. Shade in the area represented by the water. That is a "segment" of the circle. You need to find its area and then multiply by the height of the barrel (48 in) to get the volume.

 

You will have to use some trigonometry to get the area of the segment (area of sector - area of triangle) Clue: 30-60-90 right triangle relationships.

See: https://www.desmos.com/calculator/u4rxwd5ler