Question

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Mr. Harvey bought a new television that has a total surface area of 75 cubic inches. The length of the base is 7.5 inches. The width is 4 inches. What is the height of the television?
A. 2.5 inches
B. 15 inches
C. 5.5 inches
D. 3 inches

2.The surface area, S, of a right rectangular prism with length L, width W, and height H can be found using the formula below.

S=2(LW + WH + HL)

What is the surface area in square inches of a prism with a length of 12 inches, a width of 9 inches, and a height of 2 inches?
A. 92
B. 150
C. 258
D. 300

Answer 1

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.

`V=whl`
where

`V` is the volume of the rectangular prism.

`w` is the width of the base.

`l` is the length of the base.

`h` is the height of the prism.

We know from our problem that the television that has a total volume of 75 cubic inches, so
`V=75in^3`. We also know that the length of the base is 7.5 inches and the width is 4 inches, so
`l=7.5in` and
`w=4in`. Lets replace those values in our formula to find
`h`:

`V=whl`

`75in^3=(4in)(h)(7.5in)`

`75in^3=30hin^2`

`h= (75in^3)/(30in^2)`

`h=2.5in`

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:
`S=2(wl+hl+hw)`
where

`S` is the surface area of the rectangular prism.

`w` is the width.

`l` is the length.

`h` 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
`l=12in`,
`w=9in`, and
`h=2in`. Lets replace those values in our formula to find
`S`:

`S=2(wl+hl+hw)`

`S=2[(9in)(12in)+(2in)(12in)+(2in)(9in)]`

`S=2(108in^2+24in^2+18in^2)`

`S=2(150in^2)`

`S=300in^2`

We can conclude that the surface area of the prism is 300 square inches; therefore, the correct answer is: D. 300