A 9.3 pound bucket about 3/4 full of water sits on a scale that reads 95.0 pound

Question

A 9.3 pound bucket about 3/4 full of water sits on a scale that reads 95.0 pounds. A standard concrete block has two cores (as shown) and measures 7-5/8 x 7-5/8 x 15-5/8 inch on the outside. The block weighs 36.4 pounds and is lowered into the bucket and suspended by a rope that is attached to a spring scale. The block is completely in the water and no water spills out of the bucket. The spring scale reads 16.6 pounds after the concrete block is suspended in the water. Determine the following:

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4.44 pts.98%

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4.44 pts.98%

4.44 pts.98%

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4.44 pts.98%

A. The volume of the water.
(include units with answer)

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Hints: 0,0 # tries: 0 B. The weight density of the block.
(include units with answer)

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Hints: 2,0 # tries: 0 C. The material for the concrete block costs $3.50 per cubic foot. Determine the cost of a single block. ($)

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Hints: 0,0 # tries: 0 D. The reading of the scale the bucket rests on after the block is suspended.
(include units with answer)

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4.44 pts.98%

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Hints: 2,0 # tries: 0 E. The concrete block is now suspended in a new liquid. The spring scale reading is 19.3 pounds. Determine the weight density of the new liquid.
(include units with answer)

Explanation / Answer

weight of bucket = 9.3 pounds

Scale reading W = 95 pounds

mass of water, m = 95 - 9.3 = 85.7 pounds

density of water, rho = 0.0361273 pounds per cubic inch

a. so volume of water, V = m/rho = 2372.167 cu in^3

b. volume of block = V'

weight density of block = rho'

buoyant force on the block = rho*V' = 36.4 - 16.6 = 19.8 pounds

19.8 = 0.0361273*V'

V' = 548.0619 in ^3

so, weight density of block, rho' = 36.4/548.0619 = 0.06641 pounds per in^3

c. Volume of block = 548.0619 in ^3 = 548.0619/12*12*12 = 0.31716 ft^3

Cost of 1 ft^3 material = $3.5

cost of 0.31716 ft^3 material ( one blockl) = $1.11

d. After block is suspended

Reading of bucket scale = 95 + Buoyant force = 95 + 19.8 = 114.8 pounds

e. weight density of new liquid = rho"

then 36.4 - 19.3 = rho*548.0619

rho = 0.0312 pounds per cubic inch

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