Marcus found a toy that is the shape of a rectangle pyramid and is made out of plastic. The rectangular base has a length of 4cm and a width of 5cm. The height of the pyramid is 6 cm. Marcus weight the toy and finds that it is 25 grams. Find the density of the toy.

1 answer

To find the density of the toy, we can use the formula for density:

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

Where:

  • Mass = 25 grams
  • Volume = Volume of the rectangular pyramid

First, we need to calculate the volume of the rectangular pyramid. The formula for the volume \( V \) of a pyramid is:

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

The base area \( A \) of a rectangle can be calculated as:

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

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, substituting the mass and volume into the density formula:

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

Thus, the density of the toy is:

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