Therefore, the volume of the rectangular prism is 84 units cubed.

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SUMMARY

The volume of the rectangular prism is definitively calculated to be 84 cubic units. Given the surface area of 136 square units and two edge measurements of 6 and 2, the height was determined to be 7 units through the formula for surface area, A = 2(ℓw + ℓh + wh). The calculations confirm that the dimensions of the prism yield the correct volume using the formula V = ℓwh.

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What is the answer to this question. The surface area of a rectangular prism is 136 square units. Some edge measurements are 6 and 2.What is the volume?
 
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Re: Math homework

682357 said:
What is the answer to this question. The surface area of a rectangular prism is 136 square units. Some edge measurements are 6 and 2.What is the volume?
We are not here to do your homework. We can, however, guide you through.

So what have you been able to do with this problem so far?

-Dan
 
Re: Math homework

I got the answer 84units3 (or cubed)
 
Re: Math homework

682357 said:
What is the answer to this question. The surface area of a rectangular prism is 136 square units. Some edge measurements are 6 and 2.What is the volume?

682357 said:
I got the answer 84units3 (or cubed)

The dimensions are length $\ell$, width $w$ and height $h$. Suppose we know $\ell$ and $w$ to be 6 and 2 respectively. A rectangular prism (cuboid) has 3 pairs of matching faces, and it surface area $A$ is given by:

$$A=2(\ell w+\ell h+wh)$$

Using the given surface area and $\ell$ and $w$, we may state:

$$136=2(6\cdot2+6h+2h)$$

$$68=12+8h$$

$$h=7$$

And so the volume $V$ (in units cubed) is given by:

$$V=\ell wh=6\cdot2\cdot7=84\quad\checkmark$$
 

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