A trough is filled with a liquid of density 855 kg/ $\mathrm{m}^{3}$ . The ends of the trough are equilateral triangles with sides 9 m long and vertex at the bottom. Find the hydrostatic force on one end of the trough.
A) $6.79 \times 10^{5} \mathrm{~N}$
B) $7.79 \times 10^{5} \mathrm{~N}$
C) $9.79 \times 10^{5} \mathrm{~N}$
D) $8.79 \times 10^{5} \mathrm{~N}$
E) $5.79 \times 10^{5} \mathrm{~N}$

Question

Quizplus · Accepted Answer

The hydrostatic force on one end of the trough is given by:$$F = \frac{1}{2} ho g h A$$where:$$ho$$ is the density of the liquid (855 kg/m^3)$$g$$ is the acceleration due to gravity (9.8 m/s^2)$$h$$ is the height of the liquid (9 m)$$A$$ is the area of the end of the trough (the area of an equilateral triangle with sides 9 m long)$$A = \frac{\sqrt{3}}{4} s^2 = \frac{\sqrt{3}}{4} (9 \mathrm{~m})^2 = 60.33 \mathrm{~m}^2$$Substituting these values into the equation, we get:$$F = \frac{1}{2} (855 \mathrm{~kg/m}^3) (9.8 \mathrm{~m/s}^2) (9 \mathrm{~m}) (60.33 \mathrm{~m}^2) = 6.79 	imes 10^5 \mathrm{~N}$$Therefore, the correct answer is A.

A Trough Is Filled with a Liquid of Density 855 m3\mathrm{m}^{3}m3

A Trough Is Filled with a Liquid of Density 855 $\mathrm{m}^{3}$