Marcus found a toy that is in the shape of a rectangular pyramid and is made out of plastic. The rectangular base has a length of 4 cm and a width of 5 cm. The height of the pyramid is 6 cm. Marcus weighs the toy and finds that it is 25 grams. Find the density of the toy. (1 point) g/cm

1 answer

To find the density of the toy, we need to use the formula for density, which is:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

We have the mass of the toy which is given as 25 grams. Next, we need to calculate the volume of the rectangular pyramid.

The formula for the volume \( V \) of a pyramid is:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

First, we calculate the base area of the rectangular base:

\[ \text{Base Area} = \text{Length} \times \text{Width} = 4 , \text{cm} \times 5 , \text{cm} = 20 , \text{cm}^2 \]

Now we can calculate the volume of the pyramid:

\[ V = \frac{1}{3} \times 20 , \text{cm}^2 \times 6 , \text{cm} = \frac{1}{3} \times 120 , \text{cm}^3 = 40 , \text{cm}^3 \]

Now that we have the volume, we can calculate the density:

\[ \text{Density} = \frac{25 , \text{grams}}{40 , \text{cm}^3} = 0.625 , \text{g/cm}^3 \]

Thus, the density of the toy is:

\[ \boxed{0.625} , \text{g/cm}^3 \]