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Difficulty: HardCircles

A flat circular roof of a silo has a circumference of 4444 meters. A sealant must be applied to the entire top surface. If one bucket of sealant covers exactly 3030 square meters, what is the minimum number of buckets that must be purchased to seal the roof? (Use π=227\pi = \frac{22}{7})

Answer: 6 buckets

Answer

6
To find the correct number of buckets, we first derived the radius (77 meters) from the given circumference (4444 meters). Next, we calculated the total area (154154 square meters). Finally, dividing the total area by the coverage per bucket (3030 square meters) gives a value of 5.1335.133. Because we cannot purchase a fraction of a bucket and need to cover the entire roof, we must round up to 66 full buckets.

Step-by-Step Solution

1
Set up the circumference formula C=2πrC = 2\pi r using the given values to solve for the radius.
44=2×227×r44 = 2 \times \frac{22}{7} \times r, which simplifies to 44=447×r44 = \frac{44}{7} \times r. Multiplying both sides by 744\frac{7}{44} gives r=7r = 7 meters.
The radius is required to calculate the surface area of the circular roof.
2
Calculate the area of the circular roof using the formula A=πr2A = \pi r^2.
A=227×(7)2=227×49=154A = \frac{22}{7} \times (7)^2 = \frac{22}{7} \times 49 = 154 square meters.
The total area determines the total amount of sealant that is needed.
3
Determine the number of buckets needed by dividing the total area by the coverage per bucket.
154÷30=5154 \div 30 = 5 with a remainder of 44 (or 5.133...5.133...). Since partial buckets cannot be purchased, you must round up to 66 buckets.
To seal the entire surface area without leaving any sections exposed, you must purchase enough full buckets to cover the total area.

Key Concept

Calculating the area of a circle from its circumference and applying the result to a real-world scenario requiring discrete quantities.
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Topics

Circles

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