Lloyd brought a refrigerator that measures with a length of 76 centimeters, a width of 76 centimeters, and height of 170 centimeters. Lloyd plans to place the refrigerator in a space with a volume of 975,000 cubic centimeters.

Question

Part 1: Determine the volume of the refrigerator. _____ cubic centimeters (Do not round the answer and do not use commas in you answers.)
Part 2: Will the refrigerator fit in space?
Yes, the refrigerator will fit with 6,920 cubic centimeters of space left.
Yes, the refrigerator will fit with 50 cubic centimeters of space left.
No, the refrigerator will not fit. It needs at least 6,920 cubic centimeters more space.
No, the refrigerator will not fit. It needs at least 50 cubic centimeters more space.

Answer 1

To find the volume of the refrigerator, we use the formula for the volume of a rectangular prism:

\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]

Given:

• Length = 76 cm
• Width = 76 cm
• Height = 170 cm

Substituting the values into the formula:

\[ \text{Volume} = 76 , \text{cm} \times 76 , \text{cm} \times 170 , \text{cm} \] \[ \text{Volume} = 76 \times 76 = 5776 , \text{cm}^2 \] \[ \text{Volume} = 5776 \times 170 = 982920 , \text{cm}^3 \]

Part 1: The volume of the refrigerator is 982920 cubic centimeters.

Now, we check if the refrigerator will fit in the given space of 975,000 cubic centimeters.

Part 2: To see if the refrigerator fits, we compare the two volumes:

• Volume of refrigerator: 982920 cm³
• Volume of space available: 975000 cm³

Since 982920 cm³ is greater than 975000 cm³, the refrigerator will not fit.

Calculating how much more space is needed:

\[ \text{Space needed} = 982920 - 975000 = 1920 , \text{cm}^3 \]

So the answer is:

No, the refrigerator will not fit. It needs at least 1920 cubic centimeters more space.