The object below is made from a square-based pyramid joined to a cuboid - OCR - GCSE Maths - Question 8 - 2017 - Paper 1

The total height of the object is 13 cm, and the height of the cuboid is 8 cm. Thus, the height of the pyramid is:

$height_{pyramid} = total ext{ height} - height_{cuboid} = 13 - 8 = 5 ext{ cm}$

The area of the base of the pyramid is:

$Area_{base} = 4 imes 4 = 16 ext{ cm}^2$

Now, we can calculate the volume of the pyramid using the formula for the volume of a pyramid:

V_{pyramid} = rac{1}{3} imes Area_{base} imes height_{pyramid} = rac{1}{3} imes 16 imes 5 = rac{80}{3} ext{ cm}^3 ext{ or approximately } 26.67 ext{ cm}^3

We know the total mass of the object and the mass of the cuboid. The mass of the pyramid can be calculated as:

$mass_{pyramid} = total ext{ mass} - mass_{cuboid} = 158 - 85.76 ext{ g} = 72.24 ext{ g}$

Now, to find the density of the granite, we use:

density_{granite} = rac{mass_{pyramid}}{volume_{pyramid}} = rac{72.24}{rac{80}{3}} ext{ g/cm}^3

Calculating that gives:

$density_{granite} ext{ is approximately } 2.71 ext{ g/cm}^3$