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/cm3

1 answer

To find the density of the toy, we first need to calculate its volume and then use the formula for density.

  1. Volume of the rectangular pyramid: The volume \( V \) of a rectangular pyramid can be calculated using the formula:

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

where the Base Area is calculated as:

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

Now, substituting the Base Area and the height into the volume formula:

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

  1. Density calculation: Density \( \rho \) is defined as mass divided by volume:

\[ \rho = \frac{\text{mass}}{\text{volume}} = \frac{25 , \text{grams}}{40 , \text{cm}^3} \]

Calculating the density:

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

Therefore, the density of the toy is \( \boxed{0.625} , \text{g/cm}^3 \).