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QuestionA rectangular pool is 20 ft wide, 40 ft long, and 5.5 ft deep. Cost to fill it is \$12 per cubic yard. Find total cost.

Studdy Solution

STEP 1

Assumptions1. The pool is rectangular and measures20 feet wide,40 feet long, and5.5 feet deep throughout. . Each cubic yard of fill dirt costs $12.
3. The homeowner must purchase full cubic yards only, even if that means buying more than he needs.

STEP 2

First, we need to find the volume of the pool in cubic feet. We can do this by multiplying the width, length, and depth of the pool.
Volume_{ft^} = Width_{ft} \\times Length_{ft} \\times Depth_{ft}

STEP 3

Now, plug in the given values for the width, length, and depth to calculate the volume of the pool in cubic feet.
Volumeft3=20 fttimes40 fttimes5.5 ftVolume_{ft^3} =20\,ft \\times40\,ft \\times5.5\,ft

STEP 4

Calculate the volume of the pool in cubic feet.
Volumeft3=20 fttimes40 fttimes. ft=4400 ft3Volume_{ft^3} =20\,ft \\times40\,ft \\times.\,ft =4400\,ft^3

STEP 5

Next, we need to convert the volume from cubic feet to cubic yards because the fill dirt is sold by the cubic yard. There are27 cubic feet in a cubic yard.
Volumeyd3=Volumeft3/27Volume_{yd^3} = Volume_{ft^3} /27

STEP 6

Plug in the value for the volume in cubic feet to calculate the volume in cubic yards.
Volumeyd3=4400 ft3/27Volume_{yd^3} =4400\,ft^3 /27

STEP 7

Calculate the volume in cubic yards. Since the homeowner must purchase full cubic yards only, round up to the nearest whole number.
Volumeyd3=⌈4400 ft3/27⌉=163 yd3Volume_{yd^3} = \lceil4400\,ft^3 /27 \rceil =163\,yd^3

STEP 8

Now that we have the volume in cubic yards, we can find the total cost to fill in the pool. This can be found by multiplying the volume in cubic yards by the cost per cubic yard.
Cost=Volumeyd3timesCost per cubic yardCost = Volume_{yd^3} \\times Cost\, per\, cubic\, yard

STEP 9

Plug in the values for the volume in cubic yards and the cost per cubic yard to calculate the total cost.
Cost=163 yd3times$12 per yd3Cost =163\,yd^3 \\times \$12\, per\, yd^3

STEP 10

Calculate the total cost to fill in the pool.
Cost=163 yd3times$12 per yd3=$,956Cost =163\,yd^3 \\times \$12\, per\, yd^3 = \$,956The cost to fill in the pool is $,956.

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