Question

a gift box is in the shape of a right rectangular prism. the gift box is ( 7\frac{3}{5} ) centimeters long, ( 5\frac{4}{5} ) centimeters wide, and ( 2\frac{1}{2} ) centimeters high. what is the volume, in cubic centimeters, of the gift box?
a ( 15\frac{9}{10} )

b ( 70\frac{6}{25} )

c ( 110\frac{1}{5} )

d ( 155\frac{8}{50} )

Explanation:

Step1: Convert mixed numbers to improper fractions

The length is \(7\frac{3}{5}=\frac{7\times5 + 3}{5}=\frac{38}{5}\), the width is \(5\frac{4}{5}=\frac{5\times5+4}{5}=\frac{29}{5}\), and the height is \(2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}\).

Step2: Use the volume formula for a rectangular prism (\(V = l\times w\times h\))

Substitute the values into the formula: \(V=\frac{38}{5}\times\frac{29}{5}\times\frac{5}{2}\). First, simplify by canceling the 5 in the numerator of the third fraction and the denominator of the first fraction: \(V=\frac{38}{1}\times\frac{29}{5}\times\frac{1}{2}\). Then, multiply \(\frac{38}{2}\) first: \(\frac{38}{2}=19\). Now the formula becomes \(V = 19\times\frac{29}{5}\).

Step3: Multiply the remaining numbers

\(19\times\frac{29}{5}=\frac{19\times29}{5}=\frac{551}{5}\). Convert \(\frac{551}{5}\) back to a mixed number: \(551\div5 = 110\) with a remainder of 1, so \(\frac{551}{5}=110\frac{1}{5}\).

Answer:

C. \(110\frac{1}{5}\)