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A shipping container in the shape of a rectangular prism has a base with an area of 4242 square feet. The height of the container is 5345\frac{3}{4} feet. What is the volume, in cubic feet, of the shipping container?

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Full solution

Q. A shipping container in the shape of a rectangular prism has a base with an area of 4242 square feet. The height of the container is 5345\frac{3}{4} feet. What is the volume, in cubic feet, of the shipping container?
  1. Identify Formula: Identify the formula for the volume of a rectangular prism.\newlineThe volume VV of a rectangular prism is found by multiplying the area of the base BB by the height hh of the prism.\newlineThe formula is V=B×hV = B \times h.
  2. Find Base Area: Find the area of the base of the shipping container.\newlineThe problem states that the base has an area of 4242 square feet. Therefore, B=42B = 42 square feet.
  3. Convert Height to Fraction: Convert the height of the container to an improper fraction.\newlineThe height is given as 5345\frac{3}{4} feet. To convert this to an improper fraction, multiply the whole number 55 by the denominator 44 and add the numerator 33.\newline5×4+3=20+3=235 \times 4 + 3 = 20 + 3 = 23\newlineSo, the height in feet as an improper fraction is 234\frac{23}{4} feet.
  4. Calculate Volume: Calculate the volume of the shipping container.\newlineUsing the formula V=B×hV = B \times h, substitute the known values.\newlineV=42 square feet×234 feetV = 42 \text{ square feet} \times \frac{23}{4} \text{ feet}\newlineV=(42×23)/4 cubic feetV = (42 \times 23) / 4 \text{ cubic feet}\newlineV=966/4 cubic feetV = 966 / 4 \text{ cubic feet}\newlineV=241.5 cubic feetV = 241.5 \text{ cubic feet}

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