A rectangular prism has a base that is 5 cm by 7 cm and a height of 12 cm. If all dimensions are doubled, what happens to the volume?
A. When the dimensions are doubled, the volume is twice the original volume.
B. When the dimensions are doubled, the volume is three times the original volume.
C. When the dimensions are doubled, the volume is four times the original volume.
D. When the dimensions are doubled, the volume is eight times the original volume.
Yes Its D
Is it D?
volume grows by 2^3 = 8
To find the answer, we need to understand the relationship between the dimensions and volume of a rectangular prism.
The volume of a rectangular prism is calculated by multiplying its three dimensions: length (L), width (W), and height (H). So, the formula for the volume (V) of a rectangular prism is:
V = L * W * H
In this case, the original dimensions are:
Length = 5 cm
Width = 7 cm
Height = 12 cm
To determine what happens to the volume when the dimensions are doubled, we need to double each dimension:
Length (doubled) = 5 cm * 2 = 10 cm
Width (doubled) = 7 cm * 2 = 14 cm
Height (doubled) = 12 cm * 2 = 24 cm
Now, we can calculate the new volume using the doubled dimensions:
New Volume (V2) = Length (doubled) * Width (doubled) * Height (doubled)
= 10 cm * 14 cm * 24 cm
Calculating the new volume, we get:
V2 = 3360 cm^3
Therefore, the new volume (V2) is 3360 cm^3.
Now, let's compare the new volume (V2) with the original volume (V1):
Original Volume (V1) = Length * Width * Height
= 5 cm * 7 cm * 12 cm
= 420 cm^3
Comparing V2 with V1:
V2 / V1 = 3360 cm^3 / 420 cm^3
= 8
So, the new volume (V2) is 8 times the original volume (V1).
Therefore, the correct answer is option D: When the dimensions are doubled, the volume is eight times the original volume.