The height of the bucket, which has the shape of a cylinder, is 28 cm, the diameter of the bottom is 20 cm.

The height of the bucket, which has the shape of a cylinder, is 28 cm, the diameter of the bottom is 20 cm. Calculate how many square decemetres of galvanized iron were used to make the bucket, if the waste is 20% of the total harvested iron.

1. Find the surface area of ​​a bucket in the shape of a cylinder. Its surface consists of a bottom in the form of a circle and a lateral surface in the form of a rectangle, the length of which is equal to the height of the cylinder, and the width is equal to the circumference of the bottom.

Let’s find the bottom radius by the formula r = d / 2, where d is its diameter.

r = 20/2 = 10 (cm).

Find the bottom area by the formula S1 = Pr ^ 2, where П = 3.14.

S1 = P × 10 ^ 2 = 3.14 × 100 = 314 (cm ^ 2).

Let us find the length of the circle bounding the bottom by the formula L = 2Пr.

L = 2 × 3.14 × 10 = 62.8 (cm).

Let us find the area of ​​the side surface of the bucket by the formula S2 = ab, where a is the length, b is the width.

S2 = 28 × 62.8 = 1758.4 (cm ^ 2).

Find the surface area of ​​the bucket.

S = S1 + S2 = 314 + 1758.4 = 2072.4 (cm ^ 2).

2. Let’s find out what part of the material went to waste. Let us denote its area by the variable x. And since the surface area of ​​the bucket is 80%, let’s make a proportion.

2072.4 / x = 0.8 / 0.2.

Let’s solve the proportion, knowing that the product of its extreme members is equal to the product of the averages.

2072.4 x 0.2 = 0.8x;

414.48 = 0.8x;

x = 414.48 / 0.8;

x = 518.1.

3. Find how much galvanized iron is used to make a bucket.

2072.4 + 518.1 = 2590.5 (cm ^ 3) = 2.5905 (dm ^ 3).

Answer: 2.5905 dm ^ 3.