Using Cavalieri's Principle, determine which of these prisms does not have the same volume as the others?
a. dimensions 10 cm, 6 cm, 4 cm, 8 cm
b. dimensions 6 cm, 8 cm, 8 cm
c. dimensions 4 cm, 8 cm, 12 cm
d. dimensions 8 cm, 3 cm 9 cm
I got for a. 1,920, b. 384, c. 384, and d. 216 but i don't know which one is correct. obviously it would be both a and d wouldnt it? because the other two both have the same volume (b and c). which is the correct answer? i don't know what the right answer is.
Also this question must be answered by showing your work.
What is the volume of the prism?
dimensions: 8 cm, 10 cm, 8 cm, and 6 cm.
a. 192 cm^3
b. 240 cm^3
c. 320 cm^3
d. 384 cm^3
https://answers.yahoo.com/question/index?qid=20110315015615AAJTl6o
Thanks Bob! :D
To determine which prism does not have the same volume as the others, we can use Cavalieri's principle. According to the principle, if two solids have the same cross-sectional area at every height, then their volumes are equal.
Let's calculate the volumes of the given prisms step-by-step:
a. Prism with dimensions 10 cm, 6 cm, 4 cm, and 8 cm:
Volume = (10 cm) * (6 cm) * (4 cm) * (8 cm) = 1,920 cm^3
b. Prism with dimensions 6 cm, 8 cm, and 8 cm:
Volume = (6 cm) * (8 cm) * (8 cm) = 384 cm^3
c. Prism with dimensions 4 cm, 8 cm, and 12 cm:
Volume = (4 cm) * (8 cm) * (12 cm) = 384 cm^3
d. Prism with dimensions 8 cm, 3 cm, and 9 cm:
Volume = (8 cm) * (3 cm) * (9 cm) = 216 cm^3
Comparing the volumes, we see that prism a has a volume of 1,920 cm^3, prism b and prism c have volumes of 384 cm^3, and prism d has a volume of 216 cm^3.
Therefore, the prism that does not have the same volume as the others is prism a, with a volume of 1,920 cm^3.
Now, let's determine the volume of the prism with dimensions 8 cm, 10 cm, 8 cm, and 6 cm:
Volume = (8 cm) * (10 cm) * (8 cm) * (6 cm) = 3,840 cm^3
The correct answer is:
d. 3,840 cm^3
To determine which of the given prisms does not have the same volume as the others, we need to calculate the volume of each prism using their respective dimensions.
Let's start with the given prism dimensions: 10 cm, 6 cm, 4 cm, and 8 cm.
To calculate the volume using Cavalieri's Principle, we need to find the area of the base and multiply it by the height.
In this case, the base is a rectangle with dimensions 10 cm and 6 cm. So, the area of the base is 10 cm × 6 cm = 60 cm².
The height of the prism is 8 cm.
Now, multiplying the area of the base by the height, we get the volume:
Volume = Area of Base × Height
= 60 cm² × 8 cm
= 480 cm³
Therefore, the volume of prism a is 480 cm³.
Let's now calculate the volumes for the other prisms:
Prism b:
Base area = 6 cm × 8 cm = 48 cm²
Height = 8 cm
Volume = 48 cm² × 8 cm = 384 cm³
Prism c:
Base area = 4 cm × 8 cm = 32 cm²
Height = 12 cm
Volume = 32 cm² × 12 cm = 384 cm³
Prism d:
Base area = 8 cm × 3 cm = 24 cm²
Height = 9 cm
Volume = 24 cm² × 9 cm = 216 cm³
So, the volumes for the given prisms are:
a. 480 cm³
b. 384 cm³
c. 384 cm³
d. 216 cm³
From this calculation, we can see that the prism with dimensions 8 cm, 10 cm, 8 cm, and 6 cm (prism a) has a volume of 480 cm³, which is different from the volumes of the other prisms.
Hence, the correct answer is a. 480 cm³.