What fraction of a trench measuring 48m in length, 16.5m in width, and 4m in depth can be filled using the excavated soil from a cylindrical shaft of diameter 4m and length 56m?
Show answer Hide answer
Answer: B. 2/9
Explanation
Calculating the volume of the cylindrical shaft requires squaring its radius and multiplying by length. Calculating the volume of the rectangular trench involves multiplying its length, width, and depth. Dividing the shaft volume by the trench volume yields the exact fractional capacity filled. The volume of a cylinder is found using the product of pi, squared radius, and height. The volume of a rectangular trench is the product of its three linear dimensions. Excavation problems assume soil volume remains constant when transferred between different shapes.
Civil engineering earthwork calculations require matching excavated soil volume to fill requirements. Construction projects estimate material transport needs based on geometric volume conversions. Foundation digging and trenching operations rely on accurate soil displacement measurements. Option A underestimates the fraction of the trench filled by the excavated soil. Option C overestimates the proportion of the trench filled during the soil transfer. Option D is incorrect because the calculated volumetric ratio simplifies to two ninths.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. What is the proportion relating the perimeters of two square figures where the first possesses a diagonal 3 times the length of the second?
Show answer Hide answer
Answer: D. 3:1
The perimeter of any square is directly proportional to the length of its side. The diagonal of a square is directly proportional to its side length by the square root of two. Since the ratio of their diagonals is three...
Q2. What is the statistical chance that a leap year comprises exactly 53 Sundays and 52 Mondays?
Show answer Hide answer
Answer: B. 1/7
A leap year contains a total of three hundred sixty six days, which equals fifty two full weeks and two extra days. The seven possible combinations for these two extra consecutive days of the week form the sample space....
Q3. What is the initial principal sum that accumulates Rs.132 as compound interest specifically during the second year at a 10% annual rate?
Show answer Hide answer
Answer: B. Rs. 1200
Compound interest generated specifically during the second year equals the principal multiplied by rate and growth factor. Setting the growth equation with a ten percent rate yields eleven percent effective contribution...
Q4. 16 represents what percentage of 125?
Show answer Hide answer
Answer: D. None of these
Dividing sixteen by one-hundred twenty-five and multiplying by one hundred yields twelve point eight percent. Converting twelve point eight percent into a fraction gives twelve and four fifths percent. Because twelve and...
Q5. Calculate the aggregate sum of the initial 70 odd integers.
Show answer Hide answer
Answer: A. 4900
The sum of the first n positive odd integers is mathematically proven to be equal to n squared. The problem asks for the aggregate sum of the initial seventy odd integers in the number sequence. Squaring the value sevent...
Q6. In how many ways can a committee of 3 men and 2 women be chosen such that one specific man and one specific woman are invariably included?
Show answer Hide answer
Answer: C. 30
Involving one specific man and one specific woman permanently reduces the remaining selection pool requirements. Selecting two additional men from the remaining available pool requires evaluating binomial coefficient com...