a trough with triangular ends which lie in parallel planes. the top of the trough is a horizontal rectangle 50cm by 150 cm, and the depth of the trough is 40cm.

a) how many liters of water will it hold?
b) how many liters does it contain when the depth of the water is 25 cm?
c) what is the depth of the water when the through contains 12 liters?

Question

a trough with triangular ends which lie in parallel planes. the top of the trough is a horizontal rectangle 50cm by 150 cm, and the depth of the trough is 40cm.

a) how many liters of water will it hold?
b) how many liters does it contain when the depth of the water is 25 cm?
c) what is the depth of the water when the through contains 12 liters?

Vocaloid · Answer

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Vocaloid · Answer

a) consider the trough as a triangular prism, where the triangular sides are the bases and the longest side (the 150 side) is the height. area of each triangular face = (1/2)(base)(height), then multiply by the height of the prism to get volume

b) consider the volume filled by water as a smaller prism within the trough. apply the same formula as above, except you'll be using 25 cm instead of 40 as the triangle height

c) some unit conversion first: 1 L is 1000 cm^3, so 12 L is 12000 cm^3. plug this in for volume and solve for the height of the triangle.