The model of a regular quadrangular pyramid with a base side of 12 cm and a height of 20 cm is made

| June 22, 2021 | education

The model of a regular quadrangular pyramid with a base side of 12 cm and a height of 20 cm is made of the same material as the model of a ball with a radius of 6 cm. Which model is more weight?

Since the models are made of the same material, the model with the larger volume will be heavier.

Let’s calculate the volume of the pyramid. The volume of the pyramid is calculated by the formula Vp = 1/3 * Sb * h (Sb is the area of ​​the base, h is the height of the pyramid).

At the base of a regular quadrangular pyramid lies a square, which means that the area of ​​the base will be equal to: Sbasn = 12 * 12 = 144 cm².

Height h = 20 cm, hence the volume of the pyramid is Vp = 1/3 * 144 * 20 = 960 cm3.

The volume of the ball is calculated by the formula Vsh = 4/3 * n * R ^ 3.

The radius of the ball is R = 6 cm. The number n = 3.14. Find the volume of the ball:

Vsh = 4/3 * 3.14 * 6 ^ 3 = 4/3 * 3.14 * 216 = 904.32 cm3.

As you can see, the volume of the pyramid is larger, which means that its mass will be greater.

Answer: the mass of the pyramid is greater.



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