Question

Lisa is going to make a sculpture from a rectangular block of clay the volume of the block is (2x-1)(x-3)(x+4) which statement about the volume of the block is true

Answer 1

Question:

Lisa is going to make a sculpture from a rectangular block of clay. the volume of the block is (2·x – 1)(x – 3)(x + 4). which statement about the volume of the block of clay is true?

a. the volume is the product of the length, 2·x – 1, and the width, x – 3.

b. the volume does not depend on the length, 2·x – 1.

c. the volume is the product of the area of the base, (2·x – 1)(x – 3), and the height, x + 4.

d. the volume is the sum of the length, 2·x – 1, the width, x – 3, and the height, x + 4.

Answer:

The correct option is;

c. the volume is the product of the area of the base, (2·x – 1)(x – 3), and the height, x + 4.

Explanation:

Here we have the formula for the volume of rectangular block is given as;

Volume = Length × Width × Height

And the formula for the area of the base is

Area of Base = Length × Width

If the length of the rectangular block is

Length = 2·x-1 and

The width = x - 3

Therefore, the area of the base = Length × Width

= (2·x - 1) × (x -3)

From which the volume of the rectangular block can be given as

Area of base × Height

Volume = (2·x - 1) × (x -3) × (x + 4).

Answer 2

Option C is correct

C. The volume is the product of the area of the base, (2x – 1)(x – 3), and the height, x + 4.

Explanation:

Lisa is going to make a sculpture from a rectangular block of clay the volume of the block is (2x-1)(x-3)(x+4)

For a rectangular block, the volume is given as

V = (Length) × (Breadth) × (Height)

The Area of the rectangular block's base is given as

A = (Length) × (Breadth)

So, the volume of the rectangular block is now easily expressed as

V = (Area of the base of the block) × (Height)

So, if

Length = (2x-1)

Breadth = (x-3)

And height = (x+4)

Area of base = (2x-1)(x-3)

And the volume of the block will simply be

V = A × height = (2x-1)(x-3)(x+4)

And from the option, it is evident that this is the only correct option as all the other options are wrong.

Hope this Helps!!!