4) In math class, Abby learned that the ratio between the surface area of a cube and the area of one side is 6 to 1 . When Abby got a cube-shaped box in the mail, she decided to test this fact. The area of one side of the box was 20 square inches.

Question

UpStudy AI · Accepted Answer

To verify Abby's learning about the ratio between the surface area of a cube and the area of one side, we can start by using the information given.

1. **Area of one side of the cube**: 
   The area of one side of the cube is given as 20 square inches. Since the area of one side of a cube (which is a square) is calculated as $$ s^2 $$, where $$ s $$ is the length of one side of the cube, we can find $$ s $$:

$$
   s^2 = 20 \quad \Rightarrow \quad s = \sqrt{20} \quad \Rightarrow \quad s = 2\sqrt{5} \text{ inches}
   $$

2. **Surface area of the cube**: 
   The surface area $$ A $$ of a cube is given by the formula:

$$
   A = 6s^2
   $$

Substituting $$ s^2 = 20 $$:

$$
   A = 6 \times 20 = 120 \text{ square inches}
   $$

3. **Ratio of surface area to area of one side**: 
   Now, we can find the ratio of the surface area to the area of one side:

$$
   \text{Ratio} = \frac{\text{Surface Area}}{\text{Area of one side}} = \frac{120}{20} = 6
   $$

Thus, the ratio of the surface area of the cube to the area of one side is indeed 6 to 1, confirming what Abby learned in math class.
The ratio of the surface area of the cube to the area of one side is 6 to 1, confirming Abby's learning.

4) In math class, Abby learned that the ratio between the surface area of a cube and the area of one side is 6 to 1 . When Abby got a cube-shaped box in the mail, she decided to test this fact. The area of one side of the box was 20 square inches.

Real Tutor Solution

Answer

Solution

Mind Expander

Related Questions

Latest Geometry Questions