Question

a cylindrical tank 23 feet long and 9 feet in diameter is resting on its side in a horizontal position.

find the number of gallons foil in the tank if the depth of the oils 3.5?

find the total area of the cylindrical tank

Answer 1

make a sketch of the cylinder lying on its side, showing an end view.
Draw a line showing the level of oil, complete the isosceles triangle from the
centre of your circle to the end of the chord representing the level of oil.
You know the two equal sides are 4.5 ft each, they are radii, and the height
of that triangle is 1 ft

The volume of oil would the the (Area of the segment)*(23) ft^3

Let's concentrate on that segment.

Here are the steps to follow:
- Using the cosine law, you can find the central angle of the isosceles triangle, call it θ degrees.
- The sector's area is (θ/360)(π)(4/5^2)
- The area of the triangle is (1/2)(4.5)(4.5)sinθ
- subtract to get the area of the segment

volume of oil = area of segment * 23 ft^3 = ....

area of the cylinder = 2π (4.5)^2 + 2π(4.5)(23) ft^2 = ....

Answer 2

I have a typo, the line of
- The sector's area is (θ/360)(π)(4/5^2)
should say:
- The sector's area is (θ/360)(π)(4.5^2)

but I'm sure you probably recognized that anyway.