Question

some identical cylinders each have a radius of 5cm and a length of 3cm. helena has enough paint to cover 2500cm squared. how many of these cylinders can helena paint completely​

Answer 1

To find out how many of these cylinders Helena can paint completely, calculate the area covered by each cylinder, and then divide Helena's total paint area by the area covered by one cylinder. The maximum number of cylinders she can paint completely is 14.

Step-by-step explanation:

To find out how many of these cylinders Helena can paint completely, we need to calculate the area that each cylinder covers. The area of each end of the cylinder is given by the formula A = πr², where r is the radius of the cylinder. The area of the side of the cylinder is given by the formula A = 2πrh, where r is the radius and h is the length of the cylinder.

So, the total area covered by each cylinder is the sum of the areas of the two ends and the side. Since all the cylinders are identical, we can calculate the total area covered by one cylinder and then divide Helena's total paint area by that value to find out how many cylinders she can paint completely.

First, let's calculate the area of each end of the cylinder:

A = π × (5 cm)² = 25π cm²

Next, let's calculate the area of the side of the cylinder:

A = 2π × (5 cm) × (3 cm) = 30π cm²

The total area covered by one cylinder is:

A = 25π cm² + 30π cm² = 55π cm²

Now, let's divide Helena's total paint area by the area covered by one cylinder to find out how many cylinders she can paint completely:

Number of cylinders = 2500 cm² / (55π cm²) ≈ 14.39

Since she can't paint a fraction of a cylinder, the maximum number of cylinders she can paint completely is 14.

Answer 2

Helena can paint approximately 32 of these cylinders complete

Step-by-step explanation:

The surface area of a cylinder can be found using the formula:

Surface Area = 2πr(r + h), where r is the radius and h is the height (or length) of the cylinder.

For a cylinder with a radius of 5 cm and a length of 3 cm, the surface area is:

Surface Area = 2π x 5 x (5 + 3) = 2π x 5 x 8 = 80π cm²

So, the surface area of one cylinder is 80π cm². To find the number of cylinders that Helena can paint, we can divide her total paint coverage by the surface area of one cylinder:

2500 cm² ÷ 80π cm² = 31.83 (approximately 32 cylinders).

So, Helena can paint approximately 32 of these cylinders completel