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Given the cube below, which equation can be used to prove the volume of a pyramid through dissection of the cube?

c x 7 x 3 1/2 x 3 1/2 = 1/6(343)

c x 7 x 7 x 3 1/2 = 1/6(343)

c x 3 1/2 x 3 1/2 x 3 1/2 = 343

c x 7 x 7 x 7 = 343

Given the cube below which equation can be used to prove the volume of a pyramid through dissection of the cube c x 7 x 3 12 x 3 12 16343 c x 7 x 7 x 3 12 16343 class=

Respuesta :

znk

Answer:

c × 7 × 7 × 3½ = 1/6(343)  

Step-by-step explanation:

Draw the  four diagonals of the cube.

They divide the cube into six identical pyramids. I have outlined one of them for you.

The volume of the cube is

V = 7 cm × 7 cm × 7 cm  = 643 cm³

There are six pyramids, so the volume of one pyramid is  

Vₚ = ⅙ × 7 cm × 7 cm × 7 cm = ⅙(343) cm³

Also, the volume of a pyramid is directly proportional to the area of the base and to the height.

Vₚ = c × A × h, where c is some constant

A = 7 cm × 7 cm, and h = 3½ cm. So,  

Vₚ = c × 7 cm × 7 cm × 3½ cm = ⅙(343) cm³

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