Question

A concrete sphere is to be painted. It is estimated that the first coating costs about 20 pesos per square meters per worker and the second coating is about 30 pesos per square meters per worker. If the radius of the sphere is 10 meters, how much is the paint job to be accomplished by two workers?



Cost of paint job = Php

Answer 1

PHP 62,800

Step-by-step explanation:

Given: 20 pesos per square meters per worker and the second coating is about 30 pesos per square meters per worker. Radius of the sphere is 10m.

Find: Cost of paint job by two workers.

Solution: The formula to find the surface area of a sphere = 4πr² = 4 * 22/7 * 10 * 10 = 1256 square meters.

Cost of first coat = 20 * 1256 = 25120 pesos

Cost of second coat = 30 * 1256 = 37680 pesos

So total cost of paint job by two workers to finish two coatings is 62,800 pesos in total. Split this among two workers, each worker will get 31,400 pesos. The total square foot remains the same, so the total cost of painting remains the same. If there are more workers, then the total is split among them.

Answer 2

Given:

The radius of the sphere, r = 10 meters

Cost of first coating per square meter per worker = 20 pesos

Cost of second coating per square meter per worker = 30 pesos

To find:

How much is the paint job to be accomplished by two workers?

Solution:

In order to find the cost to paint a concrete sphere we will have to first find the TSA of the sphere.

The formula for the total surface area of the sphere as,

• TSA of a sphere = $4 \pi r^2$

∴ Total surface area of the concrete sphere is,

= $4\times \frac{22}{7} \times 10^2$

= $\frac{8800}{7}$

= 1257.14 m²

Also,

Total cost of painting two coats (i.e., first & second) of sphere per square meter per worker is,

= 20 + 30

= 50 pesos

Now,

The total cost of painting the concrete sphere per worker is,

= 1257.14 m² × 50 pesos

= 62857 Php approximately

∴ The total cost of painting the concrete sphere by two workers will be,

= 62857 × 2

= 125714 Php approximately

Thus, the cost of the paint job to be accomplished by two workers is 125714 Php approximately.

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