When a concrete structure is built, an engineer often performs a slump test on the concrete to ensure that it is of suitable strength and consistency. The engineer fills a truncated cone with a bottom diameter 200mm, top diameter 100mm and height 300mm with concrete. The engineer then places the cone on the ground and lifts off the cone. After period of time, she measures the amount of that the top of the cone has slumped to decide if the concrete is appropriate.
a) Original cone from which the slump test cone was derived had the height of 600m. What was the volume of the original cone? Express your answer to nearest cubic mm.
Formula to figure out the volume of the cone is -->V= 1/3ð<r2>h
This would have been quite easy if they had only given one diameter, but they have given two and I do not know which one to use. The top or bottom?
Also this is part b)
What was the volume of the slump-test cone?
Is it only the height which changes in this part. Because in the first part it was 600 and now it is 300 right? I am still unsure of which diameter to use, because there are 2.
To calculate the volume of the original cone, you need to use the height and the diameter. In this case, the original cone had a height of 600mm. However, you are correct that there are two diameters given - the bottom diameter of 200mm and the top diameter of 100mm.
To solve this, you need to use the average diameter of the cone. The average diameter is calculated by adding the bottom and top diameters and then dividing the sum by 2. So in this case, the average diameter would be (200mm + 100mm) / 2 = 150mm.
Now you can use the formula for the volume of a cone, V = (1/3)πr^2h, where r is the radius and h is the height. In this case, since you have the diameter, you need to divide it by 2 to get the radius: 150mm / 2 = 75mm.
Now you can substitute the values into the formula: V = (1/3)π(75mm)^2(600mm).
Calculate this using the value of π (approximately 3.14159) and you will get the volume of the original cone in cubic mm.
For part b) to calculate the volume of the slump-test cone, you are correct that only the height of the cone changes. So you can use the same average diameter of 150mm as calculated before, and the new height of 300mm. Apply the same formula as before to find the volume of the slump-test cone.
Remember to express your final answers to the nearest cubic mm.