Volume of Right Rectangular Prisms Quick Check

Question

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Question
Hakeem is building a box in the shape of a right rectangular prism to store his toys. It has a volume of 162,000 cubic centimeters. What is the width of the box if the height is 40 cm and the length is 90 cm?(1 point)
Responses

40 cm
40 cm

15 cm
15 cm

45 cm
45 cm

158,400 cm

Answer 1

To find the width of the box, we can use the formula for the volume of a right rectangular prism:

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

We are given the following information:

• Volume = 162,000 cubic centimeters
• Height = 40 cm
• Length = 90 cm

We can rearrange the formula to find the width:

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

Substituting in the known values:

\[ \text{width} = \frac{162,000 , \text{cm}^3}{90 , \text{cm} \times 40 , \text{cm}} \]

Calculating the denominator:

\[ 90 , \text{cm} \times 40 , \text{cm} = 3600 , \text{cm}^2 \]

Now we can calculate the width:

\[ \text{width} = \frac{162,000 , \text{cm}^3}{3600 , \text{cm}^2} \]

Calculating this gives:

\[ \text{width} = 45 , \text{cm} \]

So, the width of the box is 45 cm.