Question

10)
6 in.
2\frac{1}{5} in.
1\frac{3}{10} in.
sa =
v =

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(1\frac{3}{10}\) to improper fraction: \(1\frac{3}{10}=\frac{1\times10 + 3}{10}=\frac{13}{10}\)
Convert \(2\frac{1}{5}\) to improper fraction: \(2\frac{1}{5}=\frac{2\times5+1}{5}=\frac{11}{5}\)
The dimensions of the rectangular prism are \(l = \frac{13}{10}\) in, \(w=\frac{11}{5}\) in, \(h = 6\) in.

Step2: Calculate Surface Area (SA) of rectangular prism

The formula for the surface area of a rectangular prism is \(SA=2(lw + lh+wh)\)
First, calculate each product:

• \(lw=\frac{13}{10}\times\frac{11}{5}=\frac{143}{50}\)
• \(lh=\frac{13}{10}\times6=\frac{78}{10}=\frac{39}{5}\)
• \(wh=\frac{11}{5}\times6=\frac{66}{5}\)

Then, sum these products: \(\frac{143}{50}+\frac{39}{5}+\frac{66}{5}=\frac{143}{50}+\frac{39\times10}{5\times10}+\frac{66\times10}{5\times10}=\frac{143}{50}+\frac{390}{50}+\frac{660}{50}=\frac{143 + 390+660}{50}=\frac{1193}{50}\)

Multiply by 2: \(SA = 2\times\frac{1193}{50}=\frac{1193}{25}=47\frac{18}{25}\) square inches.

Step3: Calculate Volume (V) of rectangular prism

The formula for the volume of a rectangular prism is \(V=l\times w\times h\)
Substitute the values: \(V=\frac{13}{10}\times\frac{11}{5}\times6=\frac{13\times11\times6}{50}=\frac{858}{50}=\frac{429}{25}=17\frac{4}{25}\) cubic inches.

Answer:

Surface Area (SA) = \(47\frac{18}{25}\) square inches
Volume (V) = \(17\frac{4}{25}\) cubic inches