What is the volume of a similarly shaped paperweight if each dimension is three times as large as the smaller paperweight?A glass paperweight shaped like a pyramid has a volume of 4 cubic centimeters.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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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.

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