2. The best way to travel from the Swiss town of Thun to the Loeschental Valley by car is to drive to the village of Kandersteg and take the car-train to Goppenstein. Each train carries 70 cars and the
service runs every 12 minutes in each direction. The first trains leave at 05:00. Each train takes 4
minutes to unload and 4 minutes to load. As many as 600 cars queue for these trains at weekends. The
train journey to Goppenstein takes 20 minutes.
Arriving at the Kandersteg queue at 16:55, John is told that there will be 420 cars queuing ahead of him
once the next train has left. The service continues to run without any delays.
At what time will he arrive at Goppenstein station?

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.

none of these

step-by-step explanation:

23 + 34 add up to 57 so just inform the teacher of this really stupid mistake