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A building is constructed using bricks that can be modeled as right rectangular prisms with a dimension of 8\frac{1}{2}8 2 1 ​ in by 3\frac{1}{4}3 4 1 ​ in by 3\frac{1}{2}3 2 1 ​ in. If the bricks weight 0. 04 ounces per cubic inch and cost cost $0. 08 per ounce, find the cost of 1700 bricks. Round your answer to the nearest cent

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oladayoademosu

The cost of 1700 bricks is $5259.8

Volume of rectangular prism

Since the blocks are modeled as right rectangular prisms.

The volume of the rectangular prism is V = lbh where

  • l = length,
  • b = breadth and
  • h = height.

Since the dimensions of the bricks are 8¹/₂ ​ in by 3¹/₄​ in by 3¹/₂ ​ in

So, the volume of the brick, V = 8¹/₂ × 3¹/₄ × 3¹/₂ in³

= 17/2 × 13/4 × 7/2

= 1547/16 in³

= 96.6875 in³

Weight of each brick

If the bricks weigh 0.4 ounces per cubic inch,

The weight of the brick W = 0.4 ounces per cubic inch × volume of brick

= 0.4 o/in³ × 96.6875 in³

= 38.675 ounces per brick

Cost of each brick

Since the bricks cost $0.08 per ounce, then the cost per brick = $0.08 per ounce × 38.675 ounces per brick =

$ 3.094 per brick

Cost of 1700 bricks

So, the cost of 1700 bricks is C = price per brick × number of bricks

= $ 3.094 per brick × 1700 bricks

= $5259.8

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