A rectangular box has the dimensions #12\times 18 \times 14# inches. What's its volume? What's its surface area?

Answer 1

Volume: 3024 cubed inches
SA: 1272 squared inches

The formula for the volume of a rectangular prism/box is #l*w*h#, so the volume would be the dimensions (12, 18, 14) being multiplied.
#12*18*14=3024#
The formula for the surface area of a rectangular prism/box is #2lw+2wh+2lh#. Each of the six surfaces' areas needs to be added together. The prism's dimensions serve as the rectangles' lengths and widths. Each combination of dimensions are the lengths and widths of two rectangles (prism's length times prism's width, prism's width times prism's height, prism's length time prism's height).
#2*12*18+2*18*14+2*12*14=1272#
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Answer 2

To find the volume of the rectangular box, you multiply its length, width, and height:

[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} ]

Given:

  • Length (( L )) = 12 inches
  • Width (( W )) = 18 inches
  • Height (( H )) = 14 inches

[ \text{Volume} = 12 \times 18 \times 14 ] [ \text{Volume} = 3024 , \text{cubic inches} ]

To find the surface area of the rectangular box, you calculate the area of each of its six faces and then sum them up:

[ \text{Surface Area} = 2lw + 2lh + 2wh ]

Given:

  • Length (( L )) = 12 inches
  • Width (( W )) = 18 inches
  • Height (( H )) = 14 inches

[ \text{Surface Area} = 2(12 \times 18) + 2(12 \times 14) + 2(18 \times 14) ] [ \text{Surface Area} = 2(216) + 2(168) + 2(252) ] [ \text{Surface Area} = 432 + 336 + 504 ] [ \text{Surface Area} = 1272 , \text{square inches} ]

So, the volume of the rectangular box is ( 3024 , \text{cubic inches} ) and its surface area is ( 1272 , \text{square inches} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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