What is the volume of a similarly shaped paperweight if each dimension is three times as large as the smaller paperweight?A glass paperweight...

The small pyramid has a volume of 4
cm^3.

We will assume that the pyramid has a square
base.

Then the length of the side of the base is
(L).

Let the height be h.

We will use
the volume formula to find the dimensions.

We know that the colume
of a pyramid is given by :

V = (1/3) * L^2 *
h

==> (1/3) * L^2 * h =
4

==> L^2 * h = 12
............(1)

Now we will find the volume if the dimensions are 3
times larger.

==> L2 =
3L

==> h2 = 3h

==> V2 =
(1/3)*L2^2 * h2 = (1/3)* (3L)^2 * 3h

==> V2 = 1/3 * (9L^2) *
3 h

==> V2 = 9*L^2 * h

But from
(1) , we know that L^2 * h = 12

==> V2 = 9 *12 =
108

Then the volume of the bigger pyramid is 108 cubic
centimeter.