Question

WHICH ONE IS CORRECT?

Two cubes have edge lengths of 9 cm and 3 cm, respectively. What is the difference in volume of the two cubes?

1. 243 cm3

2. 756 cm3

3. 27 cm3

4. 702 cm3

Answer 1

The difference in volume of the two cubes is 702 cm3

Step-by-step Step-by-step explanation :

Given-

• Length of edge of one cube = 9 cm
• Length of edge of second cube = 3 cm

Now, The formula for finding volume of any cube is -

`\underline{ \boxed{ \mathfrak \red{volume \: of \: cube = {edge}^(3) }}}`

Therefore, substituting values. . .

Volume of one cube =
`{(9)}^(3)`

`\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: = 9 * 9 * 9`

`\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 729 \: {cm}^(3)`

Similarly,

Volume of second cube
`= {(3)}^(3)`

`\: \: \: \: \: \: \:\: \: \: \:\: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \:\: \: \: \: \: \: = 3 * 3 * 3`

`\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \:\: \: = 27 \: {cm}^(3)`

Now,

Difference in volume of two cubes = Volume of 1st cube - Volume of 2nd cube

`\: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \:= (729 - 27) {cm}^(3)`

`\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 702 \: {cm}^(3)`

Thus, the difference in volume of the two cubes comes out 702 cm3