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## Homework Statement

A large aquarium of height 5.00m is filled with fresh water to a depth of 2.00m. One wall of the aquarium consists of thick plastic 8.00m wide. By how much does the total force on that wall increase if the aquarium is next filled to a depth of 4.00m.

## Homework Equations

p = ρgh

p = F/A

A = hw

## The Attempt at a Solution

ρ = 0.998x10

^{3}kg/m

^{3}

g = 9.81 m/s

^{2}

h

_{1}= 2.00m

h

_{2}= 4.00m

w = 8.00m

ΔF = F

_{2}- F

_{1}

ΔF = p

_{2}A

_{2}- p

_{1}A

_{1}

ΔF = ρgh

_{2}A

_{2}- ρgh

_{1}A

_{1}

ΔF = ρg (h

_{2}A

_{2}- h

_{1}A

_{1})

ΔF = ρg (h

_{2}

^{2}w - h

_{1}

^{2}w)

ΔF = ρgw (h

_{2}

^{2}- h

_{1}

^{2})

ΔF = (.998x10

^{3}kg/m

^{3}) (9.81 m/s

^{2}) (8.00m) [ (4.00m)

^{2}- (2.00m)

^{2}]

ΔF = 9.40x10

^{5}N

Correct Answer: 4.71x10

^{5}N

Why am I double what the answer is suppose to be?