Follow the rules for working with measurements. Gravel is piled in the shape of a cone. The circumference of the base is 200 ft. The slant height is 41 ft. If the gravel weighs 3,200 lb/yd ³, how many 22-ton truckloads are needed to transport the gravel? A) 510 truckloads B) 74 truckloads C) 49 truckloads D) 86 truckloads E) 36 truckloads

Question

Quizplus · Accepted Answer

First, find the radius of the base using the circumference formula $C = 2\pi r$, where $C = 200$ ft. Solving for $r$, we get $r = \frac{200}{2\pi} = \frac{100}{\pi}$ ft. Next, calculate the volume of the cone using the formula $V = \frac{1}{3}\pi r^2 h$, where $h$ is the height. To find $h$, we use the Pythagorean theorem since the slant height, radius, and height form a right triangle: $h = \sqrt{41^2 - (\frac{100}{\pi})^2}$. After finding $h$, calculate the volume $V$, convert the volume from cubic feet to cubic yards ($1 \text{ cubic yard} = 27 \text{ cubic feet}$), and then multiply by the weight of the gravel per cubic yard to find the total weight in pounds. Finally, convert the total weight into tons ($1 \text{ ton} = 2000 \text{ lbs}$) and divide by 22 to find the number of 22-ton truckloads needed. The calculation will show that option B is the correct answer.

Follow the Rules for Working with Measurements