If a rectangular solid has a volume of 27 and at least one edge the length of 3,which of the following Must be true?
My thoughts lead me to think D is the answer,but I,m not sure??
a.The solid is a cube
b.Exactly 4 edges of the solid have a length of 3
c.Exactly 6 edges of the solid have a length of 3
d.The product of the lengths of at least one pair of edges of the solid must equal 9.
V = L*W*H = 27.
3*W*H = 27,
Divide both sides by 3:
W*H = 9. Satisfies choice "d".
V = 3*3*3 = 27. Satisfies choice "a".
Since the solid is a cube, choices a,c,
and d appears to be true.
Try to get a 2nd opinion.
To determine which of the following options must be true, let's analyze the information given in the problem.
We have a rectangular solid with a volume of 27. This means that the product of its length, width, and height is equal to 27.
Let's consider the option (a) - "The solid is a cube." For a solid to be a cube, all three of its dimensions (length, width, and height) must be equal. Since we know at least one edge has a length of 3, we cannot conclude that all three dimensions are equal. Therefore, option (a) is not necessarily true.
Moving on to option (b) - "Exactly 4 edges of the solid have a length of 3." If exactly 4 edges have a length of 3, then it means that all 4 corners of the rectangular solid are formed by edges with a length of 3. However, this does not give us enough information to determine whether the remaining dimensions are also 3. Therefore, option (b) is not necessarily true.
Now let's look at option (c) - "Exactly 6 edges of the solid have a length of 3." This option suggests that all edges of the rectangular solid have a length of 3. However, this contradicts the fact that we are given at least one edge with a length of 3 but no information about the other edges. Therefore, option (c) is not necessarily true.
Finally, consider option (d) - "The product of the lengths of at least one pair of edges of the solid must equal 9." Since we are given at least one edge with a length of 3, we can pair it with another edge of length 3 to form a rectangle. The product of the lengths of these two edges is indeed 9. Therefore, option (d) is necessarily true.
In conclusion, the only option that must be true is (d) - "The product of the lengths of at least one pair of edges of the solid must equal 9."