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.

Answer 1

To find the density of the toy, we need to calculate its volume and then use the formula for density, which is given by:

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

Step 1: Calculate the Volume of the Rectangular Pyramid

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

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

First, we need to find the area of the base. The base is a rectangle with a length of 4 cm and a width of 5 cm.

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

Now we can find the volume:

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

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

Step 2: Calculate the Density

Now that we have the mass of the toy (25 grams) and the volume (40 cm³), we can calculate the density:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{25 , \text{g}}{40 , \text{cm}^3} \]

To simplify this, divide both the numerator and the denominator by 5:

\[ \text{Density} = \frac{25 \div 5}{40 \div 5} = \frac{5}{8} , \text{g/cm}^3 \]

Final Answer

Thus, the density of the toy is:

\[ \text{Density} = \frac{5}{8} , \text{g/cm}^3 \quad \text{or} \quad 0.625 , \text{g/cm}^3 \]