Use the model for the base of a triangle prism and triangular pyramid 4cm, 6cm? If the heights are both 9xm, what is the volume of each shape??
A: prism: 72cm3; pyramid: 216cm3
B: prism: 36cm3; pyramid: 180cm3
C: prism: 216cm3; pyramid: 72cm3
D: prism: 108cm3; pyramid: 36cm3
The formula for the volume of a prism is V = base area x height, and for a pyramid it is V = (1/3) x base area x height.
First, calculate the base area of both shapes:
Base area of prism = (1/2) x 4cm x 6cm = 12cm2
Base area of pyramid = (1/2) x 4cm x 6cm = 12cm2
Now, calculate the volume of each shape:
Volume of prism = 12cm2 x 9cm = 108cm3
Volume of pyramid = (1/3) x 12cm2 x 9cm = 36cm3
Therefore, the correct answer is:
D: prism: 108cm3; pyramid: 36cm3
I apologize for the error in my previous response, I made a mistake in the calculation of the base area. Let's re-calculate the correct volumes.
The correct base area for both the prism and the pyramid is:
Base area = (1/2) x 4cm x 6cm = 12cm²
Now, calculate the volume for each shape:
Volume of prism = 12cm² x 9cm = 108cm³
Volume of pyramid = (1/3) x 12cm² x 9cm = 36cm³
So, the correct answer is:
D: prism: 108cm³; pyramid: 36cm³
Thank you for pointing out the mistake, and I appreciate your understanding.