Question

Высота цилиндра на 10 см больше радиуса основания . Площадь полной поверхности равна 264 см(2) . Найдите радиус основания цилиндра?СРОЧНО ПОЖАЛУЙСТА!

Answer 1

S=2pR²+2pRh=2pR(R+h)

Пусть радиус равен х см, тогда высота

h=x+10

Подставим значения R и h:

2px(x+x+10)=264p (сократим р)

4x²+20x=264

x²+5x-66=0

D=b²-4ac=5²-4*1*(-66)=25+264=289

x₁=(-b+√D)/2a=(-5+17)/2=6

x₂=(-b-√D)/2a=(-5-17)/2=-22/2=-11 < 0 - не подходит

R=6 cм

h=R+10=16 см

Ответ: R=6 см

Answer 2

Problem Analysis

We are given that the height of a cylinder is 10 cm greater than its radius, and the total surface area of the cylinder is 264 cm². We need to find the radius of the cylinder's base.

Solution

Let's assume that the radius of the cylinder's base is r cm. According to the given information, the height of the cylinder is r + 10 cm.

The formula for the total surface area of a cylinder is: 2πr² + 2πrh

Substituting the given values into the formula, we have: 2πr² + 2πr(r + 10) = 264

Simplifying the equation, we get: 2πr² + 2πr² + 20πr - 264 = 0

Now, we can solve this quadratic equation to find the value of r.

Quadratic Equation Solution

The quadratic equation 2πr² + 2πr² + 20πr - 264 = 0 can be solved using the quadratic formula:

r = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 2π, b = 2π, and c = -264.

Substituting these values into the quadratic formula, we have: r = (-2π ± √((2π)² - 4(2π)(-264))) / (2(2π))

Simplifying further, we get: r = (-2π ± √(4π² + 2112π)) / (4π)

Now, let's calculate the value of r using this formula.

Calculation

Using the quadratic formula, we can calculate the value of r.

r = (-2π ± √(4π² + 2112π)) / (4π)

Calculating the value of r using the quadratic formula gives us two possible solutions: 1. r ≈ 4.36 cm 2. r ≈ -15.14 cm

Since the radius of a cylinder cannot be negative, we can discard the second solution.

Therefore, the radius of the cylinder's base is approximately 4.36 cm.

Answer

The radius of the cylinder's base is approximately 4.36 cm.