Question

Ryan is going to make a sculpture from a rectangular block of clay. The volume of the block is (x + 8)(× - 3)(2x- 5).

Which statement about the volume of the block of clay is true?
height 2x - 5
width x - 3
length x + 8
• A. The volume does not depend on the length, x+ 8.
B. The volume is the product of the length, x + 8, and the width, x - 3
C. The volume is the sum of the length, x + 8, the width, x - 3, and theheight, 2х - 5.
D. The volume is the product of the area of the base, (x+ 8)(x - 3), and the height, 2x - 5.

Answer 1

The true statement about the volume of Ryan's rectangular block of clay, given its volume as (x + 8)(x - 3)(2x - 5), is D. The volume is the product of the area of the base, (x + 8)(x - 3), and the height, 2x - 5.

Step-by-step explanation:

The volume of Ryan's rectangular block of clay is given by the expression (x + 8)(x - 3)(2x - 5). From this expression, we can identify that the volume is indeed dependent on the three factors - termed as length, width, and height - which are multiplied together. Therefore, the statement that is true about the volume of the block of clay is:

D. The volume is the product of the area of the base, (x + 8)(x - 3), and the height, 2x - 5.

To understand this better, the formula for the volume of a rectangular prism, which is what the clay block resembles, is given by V = lwh, where 'l' is the length, 'w' is the width, and 'h' is the height of the prism. Given the dimensions of the clay block, we directly see the resemblance to this formula, confirming that the volume indeed is the product of its length, width, and height.