1. You have a small typo in your answer: cubic inches is a measure of volume not surface area. Since the a TV is basically a rectangular prism, we are going to use the formula for the volume of a rectangular prism to solve this.
[tex]V=whl[/tex]
where
[tex]V[/tex] is the volume of the rectangular prism.
[tex]w[/tex] is the width of the base.
[tex]l[/tex] is the length of the base.
[tex]h[/tex] is the height of the prism.
We know from our problem that the television that has a total volume of 75 cubic inches, so [tex]V=75in^3[/tex]. We also know that the length of the base is 7.5 inches and the width is 4 inches, so [tex]l=7.5in[/tex] and [tex]w=4in[/tex]. Lets replace those values in our formula to find [tex]h[/tex]:
[tex]V=whl[/tex]
[tex]75in^3=(4in)(h)(7.5in)[/tex]
[tex]75in^3=30hin^2[/tex]
[tex]h= \frac{75in^3}{30in^2} [/tex]
[tex]h=2.5in[/tex]
We can conclude that the height of the television is 2.5 inches; therefore, the correct answer is: A. 2.5 inches.
2. To solve this, we are going to use the formula for the surface area of a rectangular prism: [tex]S=2(wl+hl+hw)[/tex]
where
[tex]S[/tex] is the surface area of the rectangular prism.
[tex]w[/tex] is the width.
[tex]l[/tex] is the length.
[tex]h[/tex] is the height.
We know form our problem that the dimensions of our prism are:length of 12 inches, a width of 9 inches, and a height of 2 inches, so [tex]l=12in[/tex], [tex]w=9in[/tex], and [tex]h=2in[/tex]. Lets replace those values in our formula to find [tex]S[/tex]:
[tex]S=2(wl+hl+hw)[/tex]
[tex]S=2[(9in)(12in)+(2in)(12in)+(2in)(9in)][/tex]
[tex]S=2(108in^2+24in^2+18in^2)[/tex]
[tex]S=2(150in^2)[/tex]
[tex]S=300in^2[/tex]
We can conclude that the surface area of the prism is 300 square inches; therefore, the correct answer is: D. 300
