Question

Alex wants to know the volume of sand in an hourglass when all the sand is in the bottom, he stands a ruler up beside the hourglass and estimates the height of the cone of sand.a. What else does he need to measure to find the volume of sand? b. If the volume of sand is increasing at a constant rate, is the height increasing at a constant rate? Explain.

Answer 1

(a)

Notice that Alex measured the height of the hourglass. To find its volume he also has to measure the radius of the circumference of the base.

(b)

We know that the height and radius of the volume are directly proportional, which means if one increases then the other one also increases. Therefore, the answer is yes, if the volume of sand is increasing at a constant rate, the height is increasing at a constant rate because those magnitudes are directly proportional.