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a rectangular block is such that the sides of its base are of the length x cm and 3x cm. The sum of all the lengths of all its edges is 20cm. Find the volume.

2 Answers

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Answer: 20 - 4x^2

Explanation:

Base: x cm by 3x cm

x * 3x * unknown = 20

4x^2 * unknown = 20

unknown = 20 - 4x^2

Feel free to correct me if I'm wrong :)

User IanJ
by
7.9k points
2 votes

Answer:

15x^2 - 12x^3

Explanation:

A rectangular block has 3 parts that play into its volume. length, width and height. The question gives us length and width in the form of x and 3x, so height is what's missing.

It gives us a bit more information saying the sum of its edges is 20. We also have to ask how many lengths, widths and heights are there. That may be a bit hard to understand, but is you are looking at a block I could ask how many edges are vertical, just going up and down. These would be the heights. There are 4 total, and this goes the same for length and width, so 4*length + 4*width and 4*height = 20.

Taking that and plugging in x for length and 3x for width (or you could do it the other way around, it doesn't matter, you get:

4*x + 4*3x + 4*height = 20

4x + 12x + 4h = 20

16x + 4h = 20

4h = 20 - 16x

h = 5 - 4x

Now we have h in terms of x, which lets us easily find the volume just knowing x. To find the volume of a rectangular block you just multiply the length, width and height.

x*3x*(5-4x)

3x^2(5-4x)

15x^2 - 12x^3

Question doesn't give a specific value for x at all so you should be done there. Any number you plug in for x should get you the right answer

User Shan Mk
by
9.4k points

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