Video Transcript
A model of the Great Pyramid was made using an alloy with a density of 8.5 grams per cubic centimeter. The model is a square pyramid with a base length of 9.1 centimeters and a height of six centimeters. Determine the mass of the model pyramid in kilograms, approximating your answer to the nearest tenth.
Let’s start this question by drawing a diagram with the information we’re given. Here, we have a square pyramid with a base length of 9.1 centimeters. So we know that both the width and the length of the base will be 9.1 centimeters. We’re also told that the height is six centimeters. And this means the perpendicular height and not the slant height. We’re asked to find the mass of this model pyramid. And given that we’re already given the density of the alloy used for this model, then it may be sensible to use the mass density volume formula, which is that the mass of an object is equal to its density times its volume.
We’re not told the volume of our model pyramid, but we are given its dimensions. So let’s see if we can work out the volume. We can use the formula that the volume of a pyramid is equal to the length times the width times the height divided by three. So using the formula then to find the volume of our pyramid, since we have a square-base pyramid, the length and width are both 9.1 centimeters. And the height is six centimeters. So we have 9.1 times 9.1 times six divided by three.
We can simplify this using a calculator or a written multiplication method as 496.86 over three. And working out the division by three will give us 165.62 cubic centimeters. So now, we’ve calculated the volume of our model pyramid. We can combine it with the density that we’re given to work out the mass of the pyramid. So using the formula mass equals density times volume, we substitute in our values to get that the mass equals 8.5 times 165.62. Evaluating this will give us a value of 1407.77.
As our density was given in grams per cubic centimeter and our volume was given in cubic centimeters, then we know that the units for our mass will be in grams. However, we’re asked to give our answer of mass in kilograms, so we need to convert the units. Using the conversion that 1000 grams is equal to one kilogram means that, to change a unit in grams to kilograms, we simply divide by 1000. So 1407.77 divided by 1000 is 1.40777 kilograms. To approximate our answer to the nearest tenth then, we check if our second decimal digit is five or more. And as it is not, then this means that the final answer for the mass of this model pyramid is 1.4 kilograms.
