Question

pyramid a has a volume of 10 cubic units, a height of 5 units, and a length of 9 units for the longest edge. pyramid b has the same base area and height, but a length of 7 units for the longest edge.

what is the volume of pyramid b?

choose 1 answer:

a (\frac{490}{81}) cubic units

b (\frac{70}{9}) cubic units

c 10 cubic units

d 14 cubic units

Explanation:

Step1: Recall the volume formula for a pyramid

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

Step2: Analyze the given information for Pyramid A and Pyramid B

For Pyramid A: \( V_A = 10 \) cubic units, height \( h_A=5 \) units, and we know \( V_A=\frac{1}{3}B_Ah_A \). For Pyramid B: it has the same base area (\( B_B = B_A \)) and the same height (\( h_B=h_A = 5 \)) as Pyramid A.

Step3: Calculate the volume of Pyramid B

Since \( V=\frac{1}{3}Bh \), and for Pyramid B, \( B = B_A \) and \( h=h_A \), then \( V_B=\frac{1}{3}B_Bh_B=\frac{1}{3}B_Ah_A \). But we know that \( \frac{1}{3}B_Ah_A=V_A = 10 \) cubic units. So \( V_B = 10 \) cubic units.

Answer:

C. 10 cubic units