Chapter 1: Q41. (page 8)

For the cube, $x$ represents a positive whole number. Find the value of $x$ such that the volume of the cube and 6 times the area of one of its faces have the same value.

Short Answer

Expert verified

The length of the side of cube is $x = 6$ .

Step by step solution

Step 1. Volume of cube and area of square.

The volume of cube is $V = {(s i d e)}^{3}$ and the area of base of the cube is $V = {(s i d e)}^{3}$

Step 2. Write the equation for the given statement.

The side of cube is $x$ .

It is given that the volume of cube and 6 times the area of one of its faces have the same value.

Therefore, the required equation will be:

$x^{3} = 6 x^{2}$ .

Step 3. Simplify the equation.

$\begin{array}{l} \frac{x^{3}}{x^{2}} = \frac{6 x^{2}}{x^{2}} \\ x = 6 \end{array}$

The length of the side of cube is $x = 6$ .

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For the cube, $x$ represents a positive whole number. Find the value of $x$ such that the volume of the cube and 6 times the area of one of its faces have the same value.

Short Answer

Step by step solution

Step 1. Volume of cube and area of square.

Step 2. Write the equation for the given statement.

Step 3. Simplify the equation.

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Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

For the cube, x represents a positive whole number. Find the value of x such that the volume of the cube and 6 times the area of one of its faces have the same value.

Short Answer

Step by step solution

Step 1. Volume of cube and area of square.

Step 2. Write the equation for the given statement.

Step 3. Simplify the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Geometry

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

For the cube, $x$ represents a positive whole number. Find the value of $x$ such that the volume of the cube and 6 times the area of one of its faces have the same value.