Respuesta :
ANSWER
D. 85 1/3
EXPLANATION
The volume of a right prism is the product of the area of the base, B, and the height of the prism, h,
[tex]V=B\cdot h[/tex]In this case, the base area is 16 in² and the height is 5 1/3 in,
[tex]V=16in^2\cdot5\frac{1}{3}in[/tex]To multiply these two numbers, first, we have to convert the mixed number into an improper fraction by adding the whole and fraction parts,
[tex]5\frac{1}{3}=5+\frac{1}{3}=\frac{3\cdot5+1}{3}=\frac{15+1}{3}=\frac{16}{3}[/tex]So the volume is,
[tex]V=16\cdot\frac{16}{3}in^3=\frac{16\cdot16}{3}in^3=\frac{256}{3}in^3[/tex]Now, we have to convert this improper fraction into a mixed number. To do so, we have to find the closest multiple of 3 that is less than 256. This number is 255, so we have to write the numerator as the sum of 255 and 1 to get 256,
[tex]\frac{256}{3}=\frac{255+1}{3}[/tex]Distribute the denominator,
[tex]\frac{255+1}{3}=\frac{255}{3}+\frac{1}{3}[/tex]Simplify the first fraction,
[tex]\frac{255}{3}+\frac{1}{3}=85+\frac{1}{3}[/tex]Hence, the volume of the box is 85 1/3 cubic inches
