Question

pyramid a has a quadrilateral base, a height of 4 units, and a volume of 20 cubic units. pyramid b has the same base area, but its height is 12 units.

image of two pyramids, a (smaller) with height 4 and b (larger) with height 12

what is the volume of pyramid b?

choose 1 answer:
a 20 cubic units
b 60 cubic units
c 180 cubic units
d 540 cubic units

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Explanation:

Step1: Recall the volume formula for a pyramid

The volume \( V \) of a pyramid is given by \( V = \frac{1}{3}Bh \), where \( B \) is the base area and \( h \) is the height.

Step2: Analyze the relationship between the two pyramids

For Pyramid \( A \), we know \( V_A = 20 \) cubic units, \( h_A = 4 \) units. For Pyramid \( B \), \( B_B = B_A \) (same base area) and \( h_B = 12 \) units. Since the base area is the same, we can find the ratio of the heights and use it to find the volume of Pyramid \( B \). The ratio of the heights \( \frac{h_B}{h_A}=\frac{12}{4} = 3 \). Since the volume of a pyramid is proportional to its height (when base area is constant), the volume of Pyramid \( B \) will be 3 times the volume of Pyramid \( A \).

Step3: Calculate the volume of Pyramid \( B \)

\( V_B=3\times V_A = 3\times20 = 60 \) cubic units.

Answer:

B. 60 cubic units