Question

One dimension of a cube is increased by 1 inch to form a rectangular block.Suppose that the volume of a new block is 150 cubic inches, find the length of an edge of the cube?​

Answer 1

Answer:

Let edge of the cube be 'x' inch

In rectangular block,

Length = x + 1

Breadth = x

Height = x

According to statement

Volume of rectangular block = 150

$(x + 1) \times x \times x = 150 \\ {x}^{2} (x + 1) = 25 \times 6 \\ {x}^{2} (x + 1) = {5}^{2} (5 + 1) \\ so \: on \: comparing \\ x = 5$

Edge of cube = 5 inches

Answer 2

Given:

One dimension of a cube is increased by 1 inch to form a rectangular block.

The volume of a new block is 150 cubic inches

To find :

The length of an edge of the cube.

Solution:

Let edge of the cube be 'x' inch.

In rectangular block,

Length of the cube is increased by 1 inch.

Therefore,

Length = x + 1

Breadth = x

Height = x

Breadth and height of the cube are equal.

Volume of cube = l × b × h

The volume of a new block is 150 cubic inches

$( x+1)$ × $x$ × $x$ = 150

$x^{2} (x+1)$ = 25 × 6

$x^{2} (x+1)$ = 5² × ( 5 + 1 )

By equating the place value of x,

x = 5

Edge of the cube is 5 inches.

Final answer:

The length of an edge of the cube is 5 inches.