Question

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. pyramid a 2 cm 2.6 cm pyramid b 2.5 cm 2 cm 0.7 cm³ 1.2 cm³ 1.8 cm³ 2.3 cm³

Explanation:

Step1: Recall volume formula for pyramid

The volume formula for a pyramid is $V = \frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height. Since the bases are square, for Pyramid A with base - side length $a = 2.6$ cm, $B_A=a^2=(2.6)^2 = 6.76$ $cm^2$ and $h_A = 2$ cm. For Pyramid B with base - side length $b = 2$ cm, $B_B=b^2=(2)^2 = 4$ $cm^2$ and $h_B = 2.5$ cm.

Step2: Calculate volume of Pyramid A

$V_A=\frac{1}{3}B_Ah_A=\frac{1}{3}\times6.76\times2=\frac{13.52}{3}\approx4.5$ $cm^3$.

Step3: Calculate volume of Pyramid B

$V_B=\frac{1}{3}B_Bh_B=\frac{1}{3}\times4\times2.5=\frac{10}{3}\approx3.3$ $cm^3$.

Step4: Calculate the difference in volumes

$\Delta V=V_A - V_B\approx4.5 - 3.3 = 1.2$ $cm^3$.

Answer:

$1.2$ $cm^3$