Explanation:
so, if I understand correctly, the government is only providing the manufacturing of the 1500 tents based on the canvas that is provided by the schools.
that means the material costs are fully covered by the 50 schools and share equally between them.
therefore, our job is here to calculate the surface area of one tent (that is the amount of canvas needed for one tent) in m² (I am sure, the given base radius is 2.8 m and NOT 2.8 cm, as nobody could fit into a tent with 2×2.8 = 5.6 cm diameter - just imagine ...), multiply this by 1500 (as many tents as we need), multiply this by 120 (the price per m²), and divide this by 50 (the number of schools participating).
the surface area of a tent :
the bottom part is an open cylinder (no top area).
the top part is an open cone (no bottom area).
the area of a circle is
pi×r²
so, the bottom area of our bottom cylinder is
pi×2.8² = 7.84pi m² = 24.6300864... m²
the area of the cylinder wall/mantle is a rectangle.
just imagine top and bottom cylinders are off, and then you cut the mantle straight down and place it flat on a table : a rectangle.
the length is the circumference of the top/bottom circle, and the width is the original height of the cylinder.
so, that area is
2×pi×r (the circumference of a circle) × height
in our case
2×pi×2.8 × 3.5 = 5.6pi × 3.5 = 19.6pi m² = 61.57521601... m²
so, the surface area of the bottom cylinder is
61.57521601... + 24.6300864... =
= 7.84pi + 19.6pi = 27.44pi m² = 86.20530241... m²
now for the top cone :
the area of the outside mantle (remember, we don't need the bottom area) is
pi×r × surface height
but we got the straight inner height (2.1 m).
now, when you look at the cone directly from the side, you see that the inner height, the radius and the surface height are building a right-angled triangle. so, Pythagoras applies.
(surface height)² = (inner height)² + r² = 2.1² + 2.8² =
= 4.41 + 7.84 = 12.25
surface height = sqrt(12.25) = 3.5 m
so, our surface area is
pi×2.8 × 3.5 = 9.8pi m² = 30.78760801... m²
and so, the total surface area of one tent is
27.44pi + 9.8pi = 37.24pi m² = 116.9929104... m²
that is pretty much about 117 m².
ok, so, now we multiply this by 1500 (the number of tents) :
175,489.3656... m²
or if we go with the rounded 117 m² :
175,500 m²
now we multiply this by 120 (the price per m²) and get the total price or value for all 1500 tents :
21,058,723.88...
or if we go with the rounded value
21,060,000
and finally we divide this by 50 (the number of schools) to get the amount of money every school has to provide to get that total :
421,174.4775...
or if we go with the rounded value
421,200