Hi. Can someone please help me with this problem?
A rectangular block of metal weighs 3 oz. How many lbs will a similar block of the same metal weigh if the edges are twice as long?
think of it this way...
let the original edge be x units long
so x^3 = 3 oz
then the new edge would be 2x units and
(2x)^3 or 8x^3 would be the new volume.
so it is 8 times the original mass or 24 oz.
Where do you get the x^3 from?
volume = length x width x height
so volume = (x)(x)(x) = x^3
(2x)^3 = (2x)(2x)(2x) = 8x^3
Thanks!
Of course! I can help you with that problem. To solve it, we need to use the concept of scale factor. Let's break down the problem step by step.
Step 1: Find the scale factor
The scale factor is calculated by comparing the lengths of corresponding sides of two similar figures. In this case, we are comparing the edges of the rectangular blocks. The problem states that the edges of the second block are twice as long as the first block. Since all the edges have doubled in length, the scale factor is 2.
Step 2: Calculate the weight of the second block
To find the weight of the second block, we need to multiply the weight of the first block by the cube of the scale factor. The reason we use the cube of the scale factor is because weight is dependent on volume, and the volume of a rectangular block is determined by the product of its three dimensions (length, width, and height).
Weight of second block = (Weight of first block) × (Scale factor)^3
In this case, the weight of the first block is given as 3 oz, and the scale factor is 2. Plugging in the values, we get:
Weight of second block = 3 oz × 2^3
= 3 oz × 8
= 24 oz
Step 3: Convert ounces to pounds
To convert ounces to pounds, we need to divide the weight in ounces by the conversion factor, which is 16. Since there are 16 ounces in a pound, dividing the weight of the second block (24 oz) by 16 will give us the weight in pounds.
Weight of second block (in lbs) = 24 oz / 16
= 1.5 lbs
Therefore, a similar block of the same metal, with edges twice as long as the original block, will weigh 1.5 lbs.