Asolid right pyramid has a square base. the length of the base edge is4 cm and the height of the pyramid is 3 cm period what is the volume of the pyramid?

The volume of this pyramid is 16 cm³.

Step-by-step explanation:

The volume of a solid pyramid can be given as:

,

where

Here's how to solve this problem with calculus without using the previous formula.

Imaging cutting the square-base pyramid in half, horizontally. Each horizontal cross-section will be a square. The lengths of these squares' sides range from 0 cm to 3 cm. This length will be also be proportional to the vertical distance from the vertice of the pyramid.

Refer to the sketch attached. Let the vertical distance from the vertice be cm.

As a result, the length of a side of the square will be

.

The area of the square will be

.

Integrate the area of the horizontal cross-section with respect to

.

In other words, the volume of this pyramid is 16 cubic centimeters.

answer: i think it is (1,-2)

answer for #1 is c

answer for #2 is d

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