what is the difference of the volumes of the two oblique pyramids, both of which have square bases? round…

what is the difference of the volumes of the two oblique pyramids, both of which have square bases? round the volumes to the nearest tenth of a centimeter.\npyramid a\npyramid b\n2 cm\n2.5 cm\n2.6 cm\n2 cm\n0.7 cm³\n1.2 cm³\n1.8 cm³\n2.3 cm³

what is the difference of the volumes of the two oblique pyramids, both of which have square bases? round the volumes to the nearest tenth of a centimeter.\npyramid a\npyramid b\n2 cm\n2.5 cm\n2.6 cm\n2 cm\n0.7 cm³\n1.2 cm³\n1.8 cm³\n2.3 cm³

Answer

Answer:

A. $0.7\mathrm{cm}^3$

Explanation:

Step1: Recall volume formula

The volume formula for a pyramid is $V = \frac{1}{3}Bh$, where $B$ is the base - area and $h$ is the height. For a square - based pyramid, if the side length of the base is $s$, then $B=s^{2}$.

Step2: Calculate volume of Pyramid A

For Pyramid A, $s = 2.6\mathrm{cm}$ and $h = 2\mathrm{cm}$. First, find the base - area $B_A=s^{2}=(2.6)^{2}=6.76\mathrm{cm}^{2}$. Then, $V_A=\frac{1}{3}B_Ah=\frac{1}{3}\times6.76\times2=\frac{13.52}{3}\approx4.51\mathrm{cm}^{3}$.

Step3: Calculate volume of Pyramid B

For Pyramid B, $s = 2\mathrm{cm}$ and $h = 2.5\mathrm{cm}$. First, find the base - area $B_B=s^{2}=4\mathrm{cm}^{2}$. Then, $V_B=\frac{1}{3}B_Bh=\frac{1}{3}\times4\times2.5=\frac{10}{3}\approx3.33\mathrm{cm}^{3}$.

Step4: Calculate the difference

The difference in volumes $\Delta V=|V_A - V_B|=\left|\frac{13.52}{3}-\frac{10}{3}\right|=\frac{|13.52 - 10|}{3}=\frac{3.52}{3}\approx1.17\approx1.2\mathrm{cm}^{3}$.