Question

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Answer 1

Question 11

$\text {Volume = } 101 \dfrac{459}{729}$

Find the length:

$\text {Volume = Length}^3$

$\text {Length}^3 = 101 \dfrac{459}{729}$

$\text {Length}^3 = \dfrac{74088}{729}$

$\text {Length = } \sqrt[3]{\dfrac{74088}{729}}$

$\text {Length = } \dfrac{42}{9}$

$\text {Length = } \dfrac{14}{3}$

$\text {Length = } 4\dfrac{2}{3}  \text { m}$

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Question 12

Ratio = 2 : 3 : 4

Define x:

Let x be the constant ratio

Ratio = 2x : 3x : 4x

Solve x:

The sum of the cubes of the 3 numbers is 0.334125

(2x)³ + (3x)³ + (4x)³ = 0.334125

8x³ + 27x³ + 64x³ = 0.334125

99x³ = 0.334125

x³ = 0.003375

x = ∛0.003375

x = 0.15

Find the numbers:

2x = 2(0.15) = 0.3

3x = 3(0.15) = 0.45

4x = 4(0.15) = 0.6

Answer: The numbers are 0.3, 0.45 and 0.6

Answer 2

11) The length of each side of the box is 4.6667 m or $4\frac{2}{3}$ m

12) Three numbers are 0.30, 045, 0.60

Step-by-step explanation:

11)  Given Data

$\text {Volume of a Cubical box is} = 101 \frac{459}{729} m^{3}$

To find the length of each side of the box (L)

The formula for volume of the cube when the length is given is

Volume = Length × Length × Length  (cubic units)

Volume = Length³  (cubic units)

$101 \frac{459}{729} = \text{Length}^{3}$

$\text{Length}^{3} = \frac{74088}{729}$

$\text{Length} = \sqrt[3]{ \frac{74088}{729}}$

$\text{Length} = { \frac{42}{9}$

Length = 4.6667 m

OR $\text { Length }=4 \frac{2}{3} \mathrm{m}$

12) Given Data

Ratio of three numbers = 2x : 3x : 4x

Sum of the cubes of three number = 0.334125

To find - the numbers

(2x)³ + (3x)³ + (4x)³ = 0.334125

8x³ + 27x³ + 64x³ = 0.334125

x³ (8 + 27 + 64) = 0.334125

x³ (99) = 0.334125

$x ^{3} = \frac{0.334125}{99}$

x³ = 0.003375

$x = \sqrt[3]{0.003375}$

x = 0.15

2x = 2(0.15) = 0.30

3x = 3(0.15) = 0.45

4x = 4(0.15) = 0.60

2x : 3x : 4x = 0.30 : 045 : 0.60

Therefore the length of each side of the box is 4.6667 m or $4\frac{2}{3}$ m when the volume of the cube is $101 \frac{459}{729} m^{3}$.

Three numbers are 0.30, 045, 0.60 and their ratio is 2x: 3x:4x and sum of their cubes is 0.334125

To  Learn More ...

1) Show that the volume of a cube whose each edge measures 12m is 9 times the volume of a cuboid of dimensions 8m×6m×4m

https://brainly.in/question/6989578

2) A cuboid has volume four times the volume of a cube whose each edge is 7 m.Find the volume of the cuboid.

https://brainly.in/question/6507236