Question

Lloyd bought a refrigerator that measures
76 cm×76 cm×170 cm
76 cm×76 cm×170 cm to fit in a space with a volume of
975,000
cm
3
975,000 cm3. Will the refrigerator fit in the space? Explain.(1 point)
Responses
No, it is
6,920
cm
3
6,920 cm3 too small for the space.
No, it is 6,920 cm cubed too small for the space.
Yes, it will fit since it is smaller than the space.
Yes, it will fit since it is smaller than the space.
No, it is
6,920
cm
3
6,920 cm3 too big for the space.
No, it is 6,920 cm cubed too big for the space.
Yes, it will fit. It will be a bit tight, but that won’t matter.

Answer 1

To determine whether the refrigerator will fit in the space, we first need to calculate the volume of the refrigerator.

The volume \( V \) of a rectangular prism (which is the shape of the refrigerator) can be calculated using the formula:

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

Given the dimensions of the refrigerator:

- Length = 76 cm
- Width = 76 cm
- Height = 170 cm

Now let's calculate the volume:

\[
V = 76 \, \text{cm} \times 76 \, \text{cm} \times 170 \, \text{cm}
\]

Calculating step-by-step:

1. \( 76 \times 76 = 5776 \, \text{cm}^2 \)
2. \( 5776 \times 170 = 980920 \, \text{cm}^3 \)

So, the volume of the refrigerator is \( 980920 \, \text{cm}^3 \).

Now we need to compare this to the volume of the space, which is \( 975000 \, \text{cm}^3 \).

Next, let's see if the refrigerator volume is less than or greater than the available space:

\[
980920 \, \text{cm}^3 - 975000 \, \text{cm}^3 = 1920 \, \text{cm}^3
\]

This means that the refrigerator is too large for the space by \( 1920 \, \text{cm}^3 \).

Therefore, the correct response is:

**No, it is 1920 cm³ too big for the space.**