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. 0.7 cm3 1.2 cm3 1.8 cm3 2.3 cm3

Answer 1

The formula for the volume of the pyramid is, V = [1/3](area of the base)*height.


Pyramid A:

V = [1/3] (2.6cm)^2 * (2cm) = 4.5067 cm^3


Pyramid B:

V = [1/3](2cm)^2 * (2.5cm) =  3.3333 cm^3


Difference: 4.5067 cm^3 - 3.333 cm^3 = 1.17 cm^3


1.17 rounded to nearest tenth is 1.2.


Answer: 1.2 cm^3 

Answer 2

The difference in the volumes of the two oblique pyramids, both of which have square bases is 1.2 cm3.

The volume of the pyramid

The volume of the pyramid is defined as the one-by-three time of the area of the base and height.

$\rm Volume \ of \ pyramid =\dfrac{1}{3} \times Base \times Height$

The difference between the volumes of the two oblique pyramids, both of which have square bases.

The base of the first pyramid is 2.6 and its height is 2 cm.

The volume of the first pyramid is;

$\rm Volume \ of \ pyramid =\dfrac{1}{3} \times Base \times Height\\\\\rm Volume \ of \ pyramid =\dfrac{1}{3} \times 2.6 \times 1.6\times 2\\\\\rm Volume \ of \ pyramid = 4.5067$

And the base of the second pyramid is 2and its height is 2.5 cm.

The volume of the second pyramid is;

$\rm Volume \ of \ pyramid =\dfrac{1}{3} \times Base \times Height\\\\\rm Volume \ of \ pyramid =\dfrac{1}{3} \times 2 \times 2\times 2.5\\\\\rm Volume \ of \ pyramid = 3.3333$

The difference in the volumes of the two oblique pyramids, both of which have square bases is;

= 4.5067 - 3.333

= 1.2cm³

Hence, the difference in the volumes of the two oblique pyramids, both of which have square bases is 1.2 cm3.

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