Question

A sports store orders a box of table tennis balls . the dimensions of the box are 10 inches by 10 inches by 10 inches. inside the box, there are 6 layers of table tennis balls. each layer is made up of 6 rows and 6 columns of table tennis balls. 1.how many table tennis balls are in the box?2.write a multiplication expression to represent the volume of the box in cubic inches .3. write the expression you wrote for the volume of the box using exponents.4.Write a multiplication expression to represent the number of table tennis balls in one layer of the box.5.Write a multiplication expression to represent the number of table tennis balls in all 6 layers of the box .6. Write an expression using exponents to represent the total number of table tennis balls in the box .7. Explain how you could find the number of table tennis balls in the box .

Answer 1

Step-by-step explanation

Step 1

1.how many table tennis balls are in the box?

to find the total number of balls in the box

`\begin{gathered} Volume=side^3_{} \\ \text{Volume}=(6)^3 \\ \text{Volume}=216\text{ balls} \end{gathered}`

so, the total is 216 balls

Step 2

write a multiplication expression to represent the volume of the box in cubic inches .

`\begin{gathered} \text{Volume}=side^3 \\ \text{Volume}=(10inches)^3=(10\text{ inch}\cdot\text{ 10 inch }\cdot10\text{ inch)} \\ \text{Volume}=100\text{ cubic inches} \end{gathered}`

Step 3

write the expression you wrote for the volume of the box using exponents.

`\begin{gathered} \text{Volume}=side^3 \\ \text{Volume}=(10inches)^3 \end{gathered}`

Step 4

Write a multiplication expression to represent the number of table tennis balls in one layer of the box.

so, to find the number of table tennis balls in one layer of the box. make a multiplication

`\begin{gathered} B=6\cdot6\text{ balls} \\ B=36\text{ balls per layer} \end{gathered}`

Step 5

Write a multiplication expression to represent the number of table tennis balls in all 6 layers of the box .

`\begin{gathered} \text{Total number of balls} \\ T=B\cdot6 \\ T=36\cdot6 \\ \text{Total}=216\text{ balls} \end{gathered}`

Step 6

Write an expression using exponents to represent the total number of table tennis balls in the box .

`\text{total}=(6)^{3\text{ }}balls`